Markov chain approximations to nonsymmetric diffusions with bounded coefficients

Jean Dominique Deuschel*, Takashi Kumagai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider a certain class of nonsymmetric Markov chains and obtain heat kernel bounds and parabolic Harnack inequalities. Using the heat kernel estimates, we establish a sufficient condition for the family of Markov chains to converge to nonsymmetric diffusions. As an application, we approximate nonsymmetric diffusions in divergence form with bounded coefficients by nonsymmetric Markov chains. This extends the results by Stroock and Zheng to the nonsymmetric divergence forms.

Original languageEnglish
Pages (from-to)821-866
Number of pages46
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number6
DOIs
Publication statusPublished - 2013 Jun
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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