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Article: A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution
Title | A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution |
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Authors | |
Keywords | Absolute Continuity Chaos Expansion Exponential Integrability Feynman-Kac Formula Fractional Noise Hölder Continuity Stochastic Heat Equations |
Issue Date | 2013 |
Publisher | Elsevier 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? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/180477 |
ISSN | 2023 Impact Factor: 1.1 2023 SCImago Journal Rankings: 1.123 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Hu, Y | en_US |
dc.contributor.author | Nualart, D | en_US |
dc.contributor.author | Song, J | en_US |
dc.date.accessioned | 2013-01-28T01:38:32Z | - |
dc.date.available | 2013-01-28T01:38:32Z | - |
dc.date.issued | 2013 | en_US |
dc.identifier.citation | Stochastic Processes And Their Applications, 2013, v. 123 n. 3, p. 1083-1103 | en_US |
dc.identifier.issn | 0304-4149 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/180477 | - |
dc.description.abstract | In 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.language | eng | en_US |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/spa | en_US |
dc.relation.ispartof | Stochastic Processes and their Applications | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Absolute Continuity | en_US |
dc.subject | Chaos Expansion | en_US |
dc.subject | Exponential Integrability | en_US |
dc.subject | Feynman-Kac Formula | en_US |
dc.subject | Fractional Noise | en_US |
dc.subject | Hölder Continuity | en_US |
dc.subject | Stochastic Heat Equations | en_US |
dc.title | A nonlinear stochastic heat equation: Hölder continuity and smoothness of the density of the solution | en_US |
dc.type | Article | en_US |
dc.identifier.email | Song, J: txjsong@hku.hk | en_US |
dc.identifier.authority | Song, J=rp01700 | en_US |
dc.description.nature | postprint | en_US |
dc.identifier.doi | 10.1016/j.spa.2012.11.004 | en_US |
dc.identifier.scopus | eid_2-s2.0-84871666650 | en_US |
dc.identifier.hkuros | 220387 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-84871666650&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 123 | en_US |
dc.identifier.issue | 3 | en_US |
dc.identifier.spage | 1083 | en_US |
dc.identifier.epage | 1103 | en_US |
dc.identifier.isi | WOS:000315310900014 | - |
dc.publisher.place | Netherlands | en_US |
dc.identifier.scopusauthorid | Hu, Y=7407117772 | en_US |
dc.identifier.scopusauthorid | Nualart, D=7004476842 | en_US |
dc.identifier.scopusauthorid | Song, J=55489918300 | en_US |
dc.identifier.issnl | 0304-4149 | - |