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An Lp-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

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  • Kim, Ildoo
  • Kim, Kyeong-Hun

Abstract

In this article we present uniqueness, existence, and Lp-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type (0.1)du=(Lu+F(u))dt+Gk(u)dZtk, where L is a pseudo-differential operator and Zk are independent Lévy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an Lp-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2761-2786
    DOI: 10.1016/j.spa.2016.03.001
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    References listed on IDEAS

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    1. Krylov, N.V., 2009. "On divergence form SPDEs with VMO coefficients in a half space," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2095-2117, June.
    2. 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.
    3. Kim, Kyeong-Hun & Kim, Panki, 2012. "An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3921-3952.
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