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

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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.

Original languageEnglish
JournalStochastic Processes and their Applications
DOIs
Publication statusAccepted/In press - 2015 Mar 17

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Keywords

  • 35S10
  • 60H15
  • High-order operators
  • Lp-theory
  • Pseudo-differential operator
  • Stochastic partial differential equations driven by Lévy processes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics

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