Nonlinear Markov Semigroups and Interacting Lévy Type Processes

Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X desc...
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Autor*in:	Kolokoltsov, Vassili N. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2006

Schlagwörter:	positivity preserving measure-valued evolutions conditionally positive operators Markov models of interacting particles dynamic law of large numbers normal fluctuations rate of convergence Kinetic equations interacting stable jump-diffusions Lévy type processes coagulation-fragmentation

Übergeordnetes Werk:	Enthalten in: Journal of statistical physics - New York, NY [u.a.] : Springer Science + Business Media B.V., 1969, 126(2006), 3 vom: 05. Dez., Seite 585-642
Übergeordnetes Werk:	volume:126 ; year:2006 ; number:3 ; day:05 ; month:12 ; pages:585-642

Links:	Volltext

DOI / URN:	10.1007/s10955-006-9211-y

Katalog-ID:	SPR014940388

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520			\|a Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.
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650		4	\|a conditionally positive operators \|7 (dpeaa)DE-He213
650		4	\|a Markov models of interacting particles \|7 (dpeaa)DE-He213
650		4	\|a dynamic law of large numbers \|7 (dpeaa)DE-He213
650		4	\|a normal fluctuations \|7 (dpeaa)DE-He213
650		4	\|a rate of convergence \|7 (dpeaa)DE-He213
650		4	\|a Kinetic equations \|7 (dpeaa)DE-He213
650		4	\|a interacting stable jump-diffusions \|7 (dpeaa)DE-He213
650		4	\|a Lévy type processes \|7 (dpeaa)DE-He213
650		4	\|a coagulation-fragmentation \|7 (dpeaa)DE-He213
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allfields	10.1007/s10955-006-9211-y doi (DE-627)SPR014940388 (SPR)s10955-006-9211-y-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Kolokoltsov, Vassili N. verfasserin aut Nonlinear Markov Semigroups and Interacting Lévy Type Processes 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models. positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 126(2006), 3 vom: 05. Dez., Seite 585-642 (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:126 year:2006 number:3 day:05 month:12 pages:585-642 https://dx.doi.org/10.1007/s10955-006-9211-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 126 2006 3 05 12 585-642
spelling	10.1007/s10955-006-9211-y doi (DE-627)SPR014940388 (SPR)s10955-006-9211-y-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Kolokoltsov, Vassili N. verfasserin aut Nonlinear Markov Semigroups and Interacting Lévy Type Processes 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models. positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 126(2006), 3 vom: 05. Dez., Seite 585-642 (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:126 year:2006 number:3 day:05 month:12 pages:585-642 https://dx.doi.org/10.1007/s10955-006-9211-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 126 2006 3 05 12 585-642
allfields_unstemmed	10.1007/s10955-006-9211-y doi (DE-627)SPR014940388 (SPR)s10955-006-9211-y-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Kolokoltsov, Vassili N. verfasserin aut Nonlinear Markov Semigroups and Interacting Lévy Type Processes 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models. positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 126(2006), 3 vom: 05. Dez., Seite 585-642 (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:126 year:2006 number:3 day:05 month:12 pages:585-642 https://dx.doi.org/10.1007/s10955-006-9211-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 126 2006 3 05 12 585-642
allfieldsGer	10.1007/s10955-006-9211-y doi (DE-627)SPR014940388 (SPR)s10955-006-9211-y-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Kolokoltsov, Vassili N. verfasserin aut Nonlinear Markov Semigroups and Interacting Lévy Type Processes 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models. positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 126(2006), 3 vom: 05. Dez., Seite 585-642 (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:126 year:2006 number:3 day:05 month:12 pages:585-642 https://dx.doi.org/10.1007/s10955-006-9211-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 126 2006 3 05 12 585-642
allfieldsSound	10.1007/s10955-006-9211-y doi (DE-627)SPR014940388 (SPR)s10955-006-9211-y-e DE-627 ger DE-627 rakwb eng 530 ASE 31.00 bkl 33.00 bkl Kolokoltsov, Vassili N. verfasserin aut Nonlinear Markov Semigroups and Interacting Lévy Type Processes 2006 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models. positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213 Enthalten in Journal of statistical physics New York, NY [u.a.] : Springer Science + Business Media B.V., 1969 126(2006), 3 vom: 05. Dez., Seite 585-642 (DE-627)320578437 (DE-600)2017302-7 1572-9613 nnns volume:126 year:2006 number:3 day:05 month:12 pages:585-642 https://dx.doi.org/10.1007/s10955-006-9211-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE 33.00 ASE AR 126 2006 3 05 12 585-642
language	English
source	Enthalten in Journal of statistical physics 126(2006), 3 vom: 05. Dez., Seite 585-642 volume:126 year:2006 number:3 day:05 month:12 pages:585-642
sourceStr	Enthalten in Journal of statistical physics 126(2006), 3 vom: 05. Dez., Seite 585-642 volume:126 year:2006 number:3 day:05 month:12 pages:585-642
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	positivity preserving measure-valued evolutions conditionally positive operators Markov models of interacting particles dynamic law of large numbers normal fluctuations rate of convergence Kinetic equations interacting stable jump-diffusions Lévy type processes coagulation-fragmentation
dewey-raw	530
isfreeaccess_bool	false
container_title	Journal of statistical physics
authorswithroles_txt_mv	Kolokoltsov, Vassili N. @@aut@@
publishDateDaySort_date	2006-12-05T00:00:00Z
hierarchy_top_id	320578437
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id	SPR014940388
language_de	englisch
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author	Kolokoltsov, Vassili N.
spellingShingle	Kolokoltsov, Vassili N. ddc 530 bkl 31.00 bkl 33.00 misc positivity preserving measure-valued evolutions misc conditionally positive operators misc Markov models of interacting particles misc dynamic law of large numbers misc normal fluctuations misc rate of convergence misc Kinetic equations misc interacting stable jump-diffusions misc Lévy type processes misc coagulation-fragmentation Nonlinear Markov Semigroups and Interacting Lévy Type Processes
authorStr	Kolokoltsov, Vassili N.
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topic_title	530 ASE 31.00 bkl 33.00 bkl Nonlinear Markov Semigroups and Interacting Lévy Type Processes positivity preserving measure-valued evolutions (dpeaa)DE-He213 conditionally positive operators (dpeaa)DE-He213 Markov models of interacting particles (dpeaa)DE-He213 dynamic law of large numbers (dpeaa)DE-He213 normal fluctuations (dpeaa)DE-He213 rate of convergence (dpeaa)DE-He213 Kinetic equations (dpeaa)DE-He213 interacting stable jump-diffusions (dpeaa)DE-He213 Lévy type processes (dpeaa)DE-He213 coagulation-fragmentation (dpeaa)DE-He213
topic	ddc 530 bkl 31.00 bkl 33.00 misc positivity preserving measure-valued evolutions misc conditionally positive operators misc Markov models of interacting particles misc dynamic law of large numbers misc normal fluctuations misc rate of convergence misc Kinetic equations misc interacting stable jump-diffusions misc Lévy type processes misc coagulation-fragmentation
topic_unstemmed	ddc 530 bkl 31.00 bkl 33.00 misc positivity preserving measure-valued evolutions misc conditionally positive operators misc Markov models of interacting particles misc dynamic law of large numbers misc normal fluctuations misc rate of convergence misc Kinetic equations misc interacting stable jump-diffusions misc Lévy type processes misc coagulation-fragmentation
topic_browse	ddc 530 bkl 31.00 bkl 33.00 misc positivity preserving measure-valued evolutions misc conditionally positive operators misc Markov models of interacting particles misc dynamic law of large numbers misc normal fluctuations misc rate of convergence misc Kinetic equations misc interacting stable jump-diffusions misc Lévy type processes misc coagulation-fragmentation
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title	Nonlinear Markov Semigroups and Interacting Lévy Type Processes
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title_full	Nonlinear Markov Semigroups and Interacting Lévy Type Processes
author_sort	Kolokoltsov, Vassili N.
journal	Journal of statistical physics
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author-letter	Kolokoltsov, Vassili N.
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title_sort	nonlinear markov semigroups and interacting lévy type processes
title_auth	Nonlinear Markov Semigroups and Interacting Lévy Type Processes
abstract	Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.
abstractGer	Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.
abstract_unstemmed	Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.
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title_short	Nonlinear Markov Semigroups and Interacting Lévy Type Processes
url	https://dx.doi.org/10.1007/s10955-006-9211-y
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up_date	2024-07-04T03:32:45.291Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR014940388</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111013152.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201006s2006 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10955-006-9211-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR014940388</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10955-006-9211-y-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">33.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kolokoltsov, Vassili N.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear Markov Semigroups and Interacting Lévy Type Processes</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2006</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space Rd (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. 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