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

Ildoo Kim and Kyeong-Hun Kim

Stochastic Processes and their Applications, 2016, vol. 126, issue 9, 2761-2786

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.

Keywords: Stochastic partial differential equations driven by Lévy processes; Lp-theory; Pseudo-differential operator; High-order operators (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:9:p:2761-2786

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DOI: 10.1016/j.spa.2016.03.001

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