A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C 1-domains

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2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)440-474
Number of pages35
JournalStochastic Processes and their Applications
Volume124
Issue number1
DOIs
Publication statusPublished - 2014

Keywords

  • -theory
  • Lévy processes
  • Sobolev spaces
  • Stochastic partial differential equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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