Dynkin's isomorphism theorem and the stochastic heat equation

Nathalie Eisenbaum, Mohammud Foondun, Davar Khoshnevisan

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Consider the stochastic heat equation ∂tu = Lu + Ẇ, where L is the generator of a [Borel right] Markov process in duality. We show that the solution is locally mutually absolutely continuous with respect to a smooth perturbation of the Gaussian process that is associated, via Dynkin's isomorphism theorem, to the local times of the replica-symmetric process that corresponds to L. In the case that L is the generator of a Lévy process on Rd, our result gives a probabilistic explanation of the recent findings of Foondun et al. (Trans Am Math Soc, 2007).

Original languageEnglish
Pages (from-to)243-260
Number of pages18
JournalPotential Analysis
Volume34
Issue number3
Early online date3 Aug 2010
DOIs
Publication statusPublished - 30 Apr 2011
Externally publishedYes

Keywords

  • Dynkin's isomorphism theorem
  • local times
  • stochastic heat equation

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