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Article: A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution

TitleA nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution
Authors
KeywordsAbsolute Continuity
Chaos Expansion
Exponential Integrability
Feynman-Kac Formula
Fractional Noise
Hölder Continuity
Stochastic Heat Equations
Issue Date2013
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/spa
Citation
Stochastic Processes And Their Applications, 2013, v. 123 n. 3, p. 1083-1103 How to Cite?
AbstractIn this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman-Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an explicit expression for the Malliavin derivatives of the solutions is obtained. Based on the representation we obtain the smooth property of the density of the law of the solution. On the other hand, we also obtain the Hölder continuity of the solutions.
Persistent Identifierhttp://hdl.handle.net/10722/180477
ISSN
2015 Impact Factor: 1.193
2015 SCImago Journal Rankings: 1.664
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHu, Yen_US
dc.contributor.authorNualart, Den_US
dc.contributor.authorSong, Jen_US
dc.date.accessioned2013-01-28T01:38:32Z-
dc.date.available2013-01-28T01:38:32Z-
dc.date.issued2013en_US
dc.identifier.citationStochastic Processes And Their Applications, 2013, v. 123 n. 3, p. 1083-1103en_US
dc.identifier.issn0304-4149en_US
dc.identifier.urihttp://hdl.handle.net/10722/180477-
dc.description.abstractIn this paper, we establish a version of the Feynman-Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman-Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an explicit expression for the Malliavin derivatives of the solutions is obtained. Based on the representation we obtain the smooth property of the density of the law of the solution. On the other hand, we also obtain the Hölder continuity of the solutions.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/spaen_US
dc.relation.ispartofStochastic Processes and their Applicationsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
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.titleA nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solutionen_US
dc.typeArticleen_US
dc.identifier.emailSong, J: txjsong@hku.hken_US
dc.identifier.authoritySong, J=rp01700en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1016/j.spa.2012.11.004en_US
dc.identifier.scopuseid_2-s2.0-84871666650en_US
dc.identifier.hkuros220387-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84871666650&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume123en_US
dc.identifier.issue3en_US
dc.identifier.spage1083en_US
dc.identifier.epage1103en_US
dc.identifier.isiWOS:000315310900014-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridHu, Y=7407117772en_US
dc.identifier.scopusauthoridNualart, D=7004476842en_US
dc.identifier.scopusauthoridSong, J=55489918300en_US

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