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Article: Feynman-Kac formula for heat equation driven by fractional white noise

TitleFeynman-Kac formula for heat equation driven by fractional white noise
Authors
Hu, YNualart, DSong, J
KeywordsAbsolute Continuity
Chaos Expansion
Exponential Integrability
Feynman-Kac Formula
Fractional Noise
Hölder Continuity
Stochastic Heat Equations
Issue Date2011
PublisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aop/default.htm
Citation
Annals of Probability, 2011, v. 39 n. 1, p. 291-326 How to Cite?
DOI: http://dx.doi.org/10.1214/10-AOP547
AbstractWe establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the Hölder regularity in the space and time variables.We also derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution. © Institute of Mathematical Statistics, 2011.
Persistent Identifierhttp://hdl.handle.net/10722/180469
ISSN
0091-1798
2021 Impact Factor: 2.288
2020 SCImago Journal Rankings: 3.184
ISI Accession Number ID
WOS:000286157200008
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorHu, Yen_US
dc.contributor.authorNualart, Den_US
dc.contributor.authorSong, Jen_US
dc.date.accessioned2013-01-28T01:38:30Z-
dc.date.available2013-01-28T01:38:30Z-
dc.date.issued2011en_US
dc.identifier.citationAnnals of Probability, 2011, v. 39 n. 1, p. 291-326en_US
dc.identifier.issn0091-1798en_US
dc.identifier.urihttp://hdl.handle.net/10722/180469-
dc.description.abstractWe establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the Hölder regularity in the space and time variables.We also derive a Feynman-Kac formula for the stochastic heat equation in the Skorokhod sense and we obtain the Wiener chaos expansion of the solution. © Institute of Mathematical Statistics, 2011.en_US
dc.languageengen_US
dc.publisherInstitute of Mathematical Statistics. The Journal's web site is located at http://www.imstat.org/aop/default.htm-
dc.relation.ispartofAnnals of Probabilityen_US
dc.rights© Institute of Mathematical Statistics, 2011. This article is available online at https://doi.org/10.1214/10-AOP547-
dc.subjectAbsolute Continuityen_US
dc.subjectChaos Expansionen_US
dc.subjectExponential Integrabilityen_US
dc.subjectFeynman-Kac Formulaen_US
dc.subjectFractional Noiseen_US
dc.subjectHölder Continuityen_US
dc.subjectStochastic Heat Equationsen_US
dc.titleFeynman-Kac formula for heat equation driven by fractional white noiseen_US
dc.typeArticleen_US
dc.identifier.emailSong, J: txjsong@hku.hken_US
dc.identifier.authoritySong, J=rp01700en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1214/10-AOP547en_US
dc.identifier.scopuseid_2-s2.0-78650296391en_US
dc.identifier.hkuros220391-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78650296391&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume39en_US
dc.identifier.issue1en_US
dc.identifier.spage291en_US
dc.identifier.epage326en_US
dc.identifier.isiWOS:000286157200008-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHu, Y=7407117772en_US
dc.identifier.scopusauthoridNualart, D=7004476842en_US
dc.identifier.scopusauthoridSong, J=55489918300en_US
dc.identifier.issnl0091-1798-

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