Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation

Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time w...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Wang, Wensheng [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Quadratic variation Power variation Time fractional SPIDEs Space-time white noise Weak convergence

Anmerkung:	© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

Übergeordnetes Werk:	Enthalten in: Stochastics and partial differential equations - New York, NY : Springer, 2013, 10(2021), 2 vom: 27. Juli, Seite 582-613
Übergeordnetes Werk:	volume:10 ; year:2021 ; number:2 ; day:27 ; month:07 ; pages:582-613

Links:	Volltext

DOI / URN:	10.1007/s40072-021-00208-8

Katalog-ID:	SPR04727851X

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520			\|a Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient.
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912			\|a GBV_ILN_281
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912			\|a GBV_ILN_293
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912			\|a GBV_ILN_602
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912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
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912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
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912			\|a GBV_ILN_2113
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allfields	10.1007/s40072-021-00208-8 doi (DE-627)SPR04727851X (SPR)s40072-021-00208-8-e DE-627 ger DE-627 rakwb eng Wang, Wensheng verfasserin aut Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Enthalten in Stochastics and partial differential equations New York, NY : Springer, 2013 10(2021), 2 vom: 27. Juli, Seite 582-613 (DE-627)739215078 (DE-600)2708008-0 2194-041X nnns volume:10 year:2021 number:2 day:27 month:07 pages:582-613 https://dx.doi.org/10.1007/s40072-021-00208-8 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_65 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 10 2021 2 27 07 582-613
spelling	10.1007/s40072-021-00208-8 doi (DE-627)SPR04727851X (SPR)s40072-021-00208-8-e DE-627 ger DE-627 rakwb eng Wang, Wensheng verfasserin aut Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Enthalten in Stochastics and partial differential equations New York, NY : Springer, 2013 10(2021), 2 vom: 27. Juli, Seite 582-613 (DE-627)739215078 (DE-600)2708008-0 2194-041X nnns volume:10 year:2021 number:2 day:27 month:07 pages:582-613 https://dx.doi.org/10.1007/s40072-021-00208-8 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_65 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 10 2021 2 27 07 582-613
allfields_unstemmed	10.1007/s40072-021-00208-8 doi (DE-627)SPR04727851X (SPR)s40072-021-00208-8-e DE-627 ger DE-627 rakwb eng Wang, Wensheng verfasserin aut Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Enthalten in Stochastics and partial differential equations New York, NY : Springer, 2013 10(2021), 2 vom: 27. Juli, Seite 582-613 (DE-627)739215078 (DE-600)2708008-0 2194-041X nnns volume:10 year:2021 number:2 day:27 month:07 pages:582-613 https://dx.doi.org/10.1007/s40072-021-00208-8 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_65 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 10 2021 2 27 07 582-613
allfieldsGer	10.1007/s40072-021-00208-8 doi (DE-627)SPR04727851X (SPR)s40072-021-00208-8-e DE-627 ger DE-627 rakwb eng Wang, Wensheng verfasserin aut Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Enthalten in Stochastics and partial differential equations New York, NY : Springer, 2013 10(2021), 2 vom: 27. Juli, Seite 582-613 (DE-627)739215078 (DE-600)2708008-0 2194-041X nnns volume:10 year:2021 number:2 day:27 month:07 pages:582-613 https://dx.doi.org/10.1007/s40072-021-00208-8 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_65 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 10 2021 2 27 07 582-613
allfieldsSound	10.1007/s40072-021-00208-8 doi (DE-627)SPR04727851X (SPR)s40072-021-00208-8-e DE-627 ger DE-627 rakwb eng Wang, Wensheng verfasserin aut Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Enthalten in Stochastics and partial differential equations New York, NY : Springer, 2013 10(2021), 2 vom: 27. Juli, Seite 582-613 (DE-627)739215078 (DE-600)2708008-0 2194-041X nnns volume:10 year:2021 number:2 day:27 month:07 pages:582-613 https://dx.doi.org/10.1007/s40072-021-00208-8 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_65 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_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 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_2118 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_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 10 2021 2 27 07 582-613
language	English
source	Enthalten in Stochastics and partial differential equations 10(2021), 2 vom: 27. Juli, Seite 582-613 volume:10 year:2021 number:2 day:27 month:07 pages:582-613
sourceStr	Enthalten in Stochastics and partial differential equations 10(2021), 2 vom: 27. Juli, Seite 582-613 volume:10 year:2021 number:2 day:27 month:07 pages:582-613
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Quadratic variation Power variation Time fractional SPIDEs Space-time white noise Weak convergence
isfreeaccess_bool	false
container_title	Stochastics and partial differential equations
authorswithroles_txt_mv	Wang, Wensheng @@aut@@
publishDateDaySort_date	2021-07-27T00:00:00Z
hierarchy_top_id	739215078
id	SPR04727851X
language_de	englisch
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author	Wang, Wensheng
spellingShingle	Wang, Wensheng misc Quadratic variation misc Power variation misc Time fractional SPIDEs misc Space-time white noise misc Weak convergence Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
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topic_title	Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation Quadratic variation (dpeaa)DE-He213 Power variation (dpeaa)DE-He213 Time fractional SPIDEs (dpeaa)DE-He213 Space-time white noise (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213
topic	misc Quadratic variation misc Power variation misc Time fractional SPIDEs misc Space-time white noise misc Weak convergence
topic_unstemmed	misc Quadratic variation misc Power variation misc Time fractional SPIDEs misc Space-time white noise misc Weak convergence
topic_browse	misc Quadratic variation misc Power variation misc Time fractional SPIDEs misc Space-time white noise misc Weak convergence
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title	Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
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title_full	Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
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title_sort	variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
title_auth	Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
abstract	Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
abstractGer	Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
abstract_unstemmed	Abstract High order and fractional PDEs have become prominent in theory and in modeling many phenomena. In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. On the other hand, it builds on and complements Allouba’s earlier works on time fractional SPIDEs and their gradient. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
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title_short	Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation
url	https://dx.doi.org/10.1007/s40072-021-00208-8
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up_date	2024-07-04T02:34:23.711Z
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In this paper, we study the realized power variations for the fourth order time fractional stochastic partial integro-differential equations (SPIDEs) and their gradient, driven by the space-time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for time fractional SPIDEs and their gradient. On one hand, this work builds on the recent works on delicate analysis of variations of general Gaussian processes and stochastic heat equation driven by the space-time white noise. 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Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation

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