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

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    9 Citations (Scopus)

    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 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.

    Original languageEnglish
    Pages (from-to)2761-2786
    Number of pages26
    JournalStochastic Processes and their Applications
    Volume126
    Issue number9
    DOIs
    Publication statusPublished - 2016 Sept 1

    Bibliographical note

    Publisher Copyright:
    © 2016 Elsevier B.V.

    Keywords

    • High-order operators
    • L-theory
    • Pseudo-differential operator
    • Stochastic partial differential equations driven by Lévy processes

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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