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

Research output: Contribution to journalArticle

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 Jan 1

Fingerprint

Stochastic PDEs
Sobolev spaces
Sobolev Spaces
Lp Estimates
Weighted Sobolev Spaces
Stochastic Partial Differential Equations
Random Function
Existence and Uniqueness Results
Parabolic Partial Differential Equations
Partial differential equations
Bounded Domain
Fractional
Derivatives
Derivative
Coefficient

Keywords

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

ASJC Scopus subject areas

  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics

Cite this

A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C 1-domains. / Kim, Kyeong Hun.

In: Stochastic Processes and their Applications, Vol. 124, No. 1, 01.01.2014, p. 440-474.

Research output: Contribution to journalArticle

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