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

Kyeong-Hun Kim

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 440-474

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.

Keywords: Stochastic partial differential equations; Lévy processes; Sobolev spaces; Lp-theory (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spa.2013.08.008

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