An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes

Kyeong Hun Kim, Panki Kim

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space-time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space-time white noise.

Original languageEnglish
Pages (from-to)3921-3952
Number of pages32
JournalStochastic Processes and their Applications
Volume122
Issue number12
DOIs
Publication statusPublished - 2012 Dec 1

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Keywords

  • -theory
  • Fractional Laplacian
  • Lévy noise
  • Lévy processes
  • Stochastic partial differential equations
  • White noise

ASJC Scopus subject areas

  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics

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