dc.contributor.author | Hu, Yaozhong | |
dc.contributor.author | Nualart, David | |
dc.contributor.author | Song, Jian | |
dc.date.accessioned | 2015-03-09T21:26:07Z | |
dc.date.available | 2015-03-09T21:26:07Z | |
dc.date.issued | 2011-02-01 | |
dc.identifier.citation | Hu, Yaozhong., Nualart, David., Song, Jian. "Feynman–Kac formula for heat equation driven by fractional white noise." Ann. Probab. Volume 39, Number 1 (2011), 291-326. http://dx.doi.org/10.1214/10-AOP547. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17017 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1214/10-AOP547. | en_US |
dc.description.abstract | We 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. | en_US |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.subject | Fractional noise | en_US |
dc.subject | stochastic heat equations | en_US |
dc.subject | Feynman–Kac formula | en_US |
dc.subject | exponential integrability | en_US |
dc.subject | absolute continuity | en_US |
dc.subject | Hölder continuity | en_US |
dc.subject | chaos expansion | en_US |
dc.title | Feynman-Kac formula for the heat equation driven by fractional white noise | en_US |
dc.type | Article | |
kusw.kuauthor | Nualart, David | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1214/10-AOP547 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |