The fixed points of the multivariate smoothing transform
Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\li...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mentemeier, Sebastian [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Probability theory and related fields - Berlin : Springer, 1992, 164(2015), 1-2 vom: 21. Jan., Seite 401-458 |
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| Übergeordnetes Werk: |
volume:164 ; year:2015 ; number:1-2 ; day:21 ; month:01 ; pages:401-458 |
| Links: |
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| DOI / URN: |
10.1007/s00440-015-0615-y |
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| Katalog-ID: |
SPR006006221 |
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| 100 | 1 | |a Mentemeier, Sebastian |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The fixed points of the multivariate smoothing transform |
| 264 | 1 | |c 2015 | |
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| 520 | |a Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. | ||
| 650 | 4 | |a Smoothing transform |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Markov random walks |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a General branching processes |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multivariate stable laws |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Multitype branching random walk |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Choquet–Deny lemma |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Weighted branching |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t Probability theory and related fields |d Berlin : Springer, 1992 |g 164(2015), 1-2 vom: 21. Jan., Seite 401-458 |w (DE-627)254638791 |w (DE-600)1462994-X |x 1432-2064 |7 nnns |
| 773 | 1 | 8 | |g volume:164 |g year:2015 |g number:1-2 |g day:21 |g month:01 |g pages:401-458 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00440-015-0615-y |z lizenzpflichtig |3 Volltext |
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10.1007/s00440-015-0615-y doi (DE-627)SPR006006221 (SPR)s00440-015-0615-y-e DE-627 ger DE-627 rakwb eng Mentemeier, Sebastian verfasserin aut The fixed points of the multivariate smoothing transform 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 Enthalten in Probability theory and related fields Berlin : Springer, 1992 164(2015), 1-2 vom: 21. Jan., Seite 401-458 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 https://dx.doi.org/10.1007/s00440-015-0615-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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 AR 164 2015 1-2 21 01 401-458 |
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10.1007/s00440-015-0615-y doi (DE-627)SPR006006221 (SPR)s00440-015-0615-y-e DE-627 ger DE-627 rakwb eng Mentemeier, Sebastian verfasserin aut The fixed points of the multivariate smoothing transform 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 Enthalten in Probability theory and related fields Berlin : Springer, 1992 164(2015), 1-2 vom: 21. Jan., Seite 401-458 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 https://dx.doi.org/10.1007/s00440-015-0615-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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 AR 164 2015 1-2 21 01 401-458 |
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10.1007/s00440-015-0615-y doi (DE-627)SPR006006221 (SPR)s00440-015-0615-y-e DE-627 ger DE-627 rakwb eng Mentemeier, Sebastian verfasserin aut The fixed points of the multivariate smoothing transform 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 Enthalten in Probability theory and related fields Berlin : Springer, 1992 164(2015), 1-2 vom: 21. Jan., Seite 401-458 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 https://dx.doi.org/10.1007/s00440-015-0615-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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 AR 164 2015 1-2 21 01 401-458 |
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10.1007/s00440-015-0615-y doi (DE-627)SPR006006221 (SPR)s00440-015-0615-y-e DE-627 ger DE-627 rakwb eng Mentemeier, Sebastian verfasserin aut The fixed points of the multivariate smoothing transform 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 Enthalten in Probability theory and related fields Berlin : Springer, 1992 164(2015), 1-2 vom: 21. Jan., Seite 401-458 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 https://dx.doi.org/10.1007/s00440-015-0615-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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 AR 164 2015 1-2 21 01 401-458 |
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10.1007/s00440-015-0615-y doi (DE-627)SPR006006221 (SPR)s00440-015-0615-y-e DE-627 ger DE-627 rakwb eng Mentemeier, Sebastian verfasserin aut The fixed points of the multivariate smoothing transform 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 Enthalten in Probability theory and related fields Berlin : Springer, 1992 164(2015), 1-2 vom: 21. Jan., Seite 401-458 (DE-627)254638791 (DE-600)1462994-X 1432-2064 nnns volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 https://dx.doi.org/10.1007/s00440-015-0615-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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 AR 164 2015 1-2 21 01 401-458 |
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Enthalten in Probability theory and related fields 164(2015), 1-2 vom: 21. Jan., Seite 401-458 volume:164 year:2015 number:1-2 day:21 month:01 pages:401-458 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006006221</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230507175115.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201002s2015 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00440-015-0615-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006006221</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00440-015-0615-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="100" ind1="1" ind2=" "><subfield code="a">Mentemeier, Sebastian</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The fixed points of the multivariate smoothing transform</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</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="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag Berlin Heidelberg 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Smoothing transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Markov random walks</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">General branching processes</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multivariate stable laws</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multitype branching random walk</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Choquet–Deny lemma</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weighted branching</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Probability theory and related fields</subfield><subfield code="d">Berlin : Springer, 1992</subfield><subfield code="g">164(2015), 1-2 vom: 21. 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Mentemeier, Sebastian |
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Mentemeier, Sebastian misc Smoothing transform misc Markov random walks misc General branching processes misc Multivariate stable laws misc Multitype branching random walk misc Choquet–Deny lemma misc Weighted branching The fixed points of the multivariate smoothing transform |
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The fixed points of the multivariate smoothing transform Smoothing transform (dpeaa)DE-He213 Markov random walks (dpeaa)DE-He213 General branching processes (dpeaa)DE-He213 Multivariate stable laws (dpeaa)DE-He213 Multitype branching random walk (dpeaa)DE-He213 Choquet–Deny lemma (dpeaa)DE-He213 Weighted branching (dpeaa)DE-He213 |
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fixed points of the multivariate smoothing transform |
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The fixed points of the multivariate smoothing transform |
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Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. © Springer-Verlag Berlin Heidelberg 2015 |
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Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. © Springer-Verlag Berlin Heidelberg 2015 |
| abstract_unstemmed |
Abstract Let %$(\mathbf {T}_1, \mathbf {T}_2, \ldots )%$ be a sequence of random %$d\times d%$ matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors %$X%$ with nonnegative entries, satisfying *X=L∑i≥1TiXi+Q,%$\begin{aligned} X\mathop {=}\limits ^{{\mathcal {L}}}\sum _{i \ge 1} \mathbf {T}_i X_i + Q, \end{aligned}%$where %$\mathop {=}\limits ^{{\mathcal {L}}}%$ denotes equality of the corresponding laws, %$(X_i)_{i \ge 1}%$ are i.i.d. copies of %$X%$ and independent of %$(Q, \mathbf {T}_1, \mathbf {T}_2, \ldots )%$. For %$d=1%$, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumptions similar to the one-dimensional case, we obtain a complete characterization of all solutions %$X%$ to (*) in the non-critical case, and existence results in the critical case. © Springer-Verlag Berlin Heidelberg 2015 |
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The fixed points of the multivariate smoothing transform |
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| score |
7.4003096 |