Premium
Markov Chain Approximations to Nonsymmetric Diffusions with Bounded Coefficients
Author(s) -
Deuschel JeanDominique,
Kumagai Takashi
Publication year - 2013
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21447
Subject(s) - mathematics , markov chain , bounded function , kernel (algebra) , divergence (linguistics) , harnack's inequality , heat kernel , markov process , pure mathematics , mathematical analysis , statistics , linguistics , philosophy
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. © 2012 Wiley Periodicals, Inc.