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A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C1-domains

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  • Kim, Kyeong-Hun

Abstract

In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on Rd, R+d and bounded C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.

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  • Kim, Kyeong-Hun, 2014. "A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C1-domains," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 440-474.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:440-474
    DOI: 10.1016/j.spa.2013.08.008
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    References listed on IDEAS

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    1. Kim, Kyeong-Hun, 2004. "On stochastic partial differential equations with variable coefficients in C1 domains," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 261-283, August.
    2. Kim, Kyeong-Hun, 2004. "Lq(Lp) theory and Hölder estimates for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 313-330, December.
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    Cited by:

    1. Kim, Ildoo & Kim, Kyeong-Hun, 2016. "An Lp-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2761-2786.

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