Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion

Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respe...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	van Neerven, J. M. A. M. [verfasserIn] Weis, L. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2008

Schlagwörter:	Stochastic integration in Banach spaces -Radonifying operators Property( ) Measurable linear extensions Stochastic evolution equations

Übergeordnetes Werk:	Enthalten in: Potential analysis - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992, 29(2008), 1 vom: 12. Juni
Übergeordnetes Werk:	volume:29 ; year:2008 ; number:1 ; day:12 ; month:06

Links:	Volltext

DOI / URN:	10.1007/s11118-008-9088-2

Katalog-ID:	SPR016844394

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520			\|a Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion.
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650		4	\|a Measurable linear extensions \|7 (dpeaa)DE-He213
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700	1		\|a Weis, L. \|e verfasserin \|4 aut
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matchkey_str	article:1572929X:2008----::tcatcnertoooeaovlefntosihepctbncs
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allfields	10.1007/s11118-008-9088-2 doi (DE-627)SPR016844394 (SPR)s11118-008-9088-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl 31.70 bkl van Neerven, J. M. A. M. verfasserin aut Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213 Weis, L. verfasserin aut Enthalten in Potential analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 29(2008), 1 vom: 12. Juni (DE-627)269758720 (DE-600)1475719-9 1572-929X nnns volume:29 year:2008 number:1 day:12 month:06 https://dx.doi.org/10.1007/s11118-008-9088-2 kostenfrei 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_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_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_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 31.40 ASE 31.70 ASE AR 29 2008 1 12 06
spelling	10.1007/s11118-008-9088-2 doi (DE-627)SPR016844394 (SPR)s11118-008-9088-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl 31.70 bkl van Neerven, J. M. A. M. verfasserin aut Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213 Weis, L. verfasserin aut Enthalten in Potential analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 29(2008), 1 vom: 12. Juni (DE-627)269758720 (DE-600)1475719-9 1572-929X nnns volume:29 year:2008 number:1 day:12 month:06 https://dx.doi.org/10.1007/s11118-008-9088-2 kostenfrei 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_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_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_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 31.40 ASE 31.70 ASE AR 29 2008 1 12 06
allfields_unstemmed	10.1007/s11118-008-9088-2 doi (DE-627)SPR016844394 (SPR)s11118-008-9088-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl 31.70 bkl van Neerven, J. M. A. M. verfasserin aut Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213 Weis, L. verfasserin aut Enthalten in Potential analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 29(2008), 1 vom: 12. Juni (DE-627)269758720 (DE-600)1475719-9 1572-929X nnns volume:29 year:2008 number:1 day:12 month:06 https://dx.doi.org/10.1007/s11118-008-9088-2 kostenfrei 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_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_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_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 31.40 ASE 31.70 ASE AR 29 2008 1 12 06
allfieldsGer	10.1007/s11118-008-9088-2 doi (DE-627)SPR016844394 (SPR)s11118-008-9088-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl 31.70 bkl van Neerven, J. M. A. M. verfasserin aut Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213 Weis, L. verfasserin aut Enthalten in Potential analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 29(2008), 1 vom: 12. Juni (DE-627)269758720 (DE-600)1475719-9 1572-929X nnns volume:29 year:2008 number:1 day:12 month:06 https://dx.doi.org/10.1007/s11118-008-9088-2 kostenfrei 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_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_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_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 31.40 ASE 31.70 ASE AR 29 2008 1 12 06
allfieldsSound	10.1007/s11118-008-9088-2 doi (DE-627)SPR016844394 (SPR)s11118-008-9088-2-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl 31.70 bkl van Neerven, J. M. A. M. verfasserin aut Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion. Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213 Weis, L. verfasserin aut Enthalten in Potential analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 29(2008), 1 vom: 12. Juni (DE-627)269758720 (DE-600)1475719-9 1572-929X nnns volume:29 year:2008 number:1 day:12 month:06 https://dx.doi.org/10.1007/s11118-008-9088-2 kostenfrei 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_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_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_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 31.40 ASE 31.70 ASE AR 29 2008 1 12 06
language	English
source	Enthalten in Potential analysis 29(2008), 1 vom: 12. Juni volume:29 year:2008 number:1 day:12 month:06
sourceStr	Enthalten in Potential analysis 29(2008), 1 vom: 12. Juni volume:29 year:2008 number:1 day:12 month:06
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Stochastic integration in Banach spaces -Radonifying operators Property( ) Measurable linear extensions Stochastic evolution equations
dewey-raw	510
isfreeaccess_bool	true
container_title	Potential analysis
authorswithroles_txt_mv	van Neerven, J. M. A. M. @@aut@@ Weis, L. @@aut@@
publishDateDaySort_date	2008-06-12T00:00:00Z
hierarchy_top_id	269758720
dewey-sort	3510
id	SPR016844394
language_de	englisch
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We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. 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author	van Neerven, J. M. A. M.
spellingShingle	van Neerven, J. M. A. M. ddc 510 bkl 31.40 bkl 31.70 misc Stochastic integration in Banach spaces misc -Radonifying operators misc Property( misc ) misc Measurable linear extensions misc Stochastic evolution equations Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
authorStr	van Neerven, J. M. A. M.
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topic_title	510 ASE 31.40 bkl 31.70 bkl Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion Stochastic integration in Banach spaces (dpeaa)DE-He213 -Radonifying operators (dpeaa)DE-He213 Property( (dpeaa)DE-He213 ) (dpeaa)DE-He213 Measurable linear extensions (dpeaa)DE-He213 Stochastic evolution equations (dpeaa)DE-He213
topic	ddc 510 bkl 31.40 bkl 31.70 misc Stochastic integration in Banach spaces misc -Radonifying operators misc Property( misc ) misc Measurable linear extensions misc Stochastic evolution equations
topic_unstemmed	ddc 510 bkl 31.40 bkl 31.70 misc Stochastic integration in Banach spaces misc -Radonifying operators misc Property( misc ) misc Measurable linear extensions misc Stochastic evolution equations
topic_browse	ddc 510 bkl 31.40 bkl 31.70 misc Stochastic integration in Banach spaces misc -Radonifying operators misc Property( misc ) misc Measurable linear extensions misc Stochastic evolution equations
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title	Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
ctrlnum	(DE-627)SPR016844394 (SPR)s11118-008-9088-2-e
title_full	Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
author_sort	van Neerven, J. M. A. M.
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author_browse	van Neerven, J. M. A. M. Weis, L.
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author-letter	van Neerven, J. M. A. M.
doi_str_mv	10.1007/s11118-008-9088-2
dewey-full	510
author2-role	verfasserin
title_sort	stochastic integration of operator-valued functions with respect to banach space-valued brownian motion
title_auth	Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
abstract	Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion.
abstractGer	Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion.
abstract_unstemmed	Abstract Let E be a real Banach space with property (α) and let WΓ be an E-valued Brownian motion with distribution Γ. We show that a function $\Psi:[0,T]\to{\mathcal L}(E)$ is stochastically integrable with respect to WΓ if and only if Γ-almost all orbits Ψx are stochastically integrable with respect to a real Brownian motion. This result is derived from an abstract result on existence of Γ-measurable linear extensions of γ-radonifying operators with values in spaces of γ-radonifying operators. As an application we obtain a necessary and sufficient condition for solvability of stochastic evolution equations driven by an E-valued Brownian motion.
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container_issue	1
title_short	Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion
url	https://dx.doi.org/10.1007/s11118-008-9088-2
remote_bool	true
author2	Weis, L.
author2Str	Weis, L.
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doi_str	10.1007/s11118-008-9088-2
up_date	2024-07-04T01:08:25.822Z
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Stochastic Integration of Operator-Valued Functions with Respect to Banach Space-Valued Brownian Motion

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