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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.

Suggested Citation

  • 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. "Lq(Lp) theory and Hölder estimates for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 313-330, December.
    2. 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.
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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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