On a class of stochastic partial differential equations

Jian Song

Stochastic Processes and their Applications, 2017, vol. 127, issue 1, 37-79

Abstract: This paper concerns the stochastic partial differential equation with multiplicative noise ∂u∂t=Lu+uẆ, where L is the generator of a symmetric Lévy process X, Ẇ is a Gaussian noise and uẆ is understood both in the senses of Stratonovich and Skorohod. The Feynman–Kac type of representations for the solutions and the moments of the solutions are obtained, and the Hölder continuity of the solutions is also studied. As a byproduct, when γ(x) is a nonnegative and nonnegative-definite function, a sufficient and necessary condition for ∫0t∫0t|r−s|−β0γ(Xr−Xs)drds to be exponentially integrable is obtained.

Keywords: Stochastic partial differential equation; Gaussian noise; Feynman–Kac formula; Malliavin calculus (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:1:p:37-79

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DOI: 10.1016/j.spa.2016.05.008

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