Markov chain approximations to symmetric diffusions
نویسندگان
چکیده
منابع مشابه
Markov chain approximations to non-symmetric diffusions with bounded coefficients
We consider a certain class of non-symmetric 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 non-symmetric diffusions. As an application, we approximate non-symmetric diffusions in divergence form with bounded coefficients by non-symmetric Markov ch...
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Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space Rd the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space Hα/2(Rd), α ∈ (0, 2), that is equivalent to the standard one.
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincare (B) Probability and Statistics
سال: 1997
ISSN: 0246-0203
DOI: 10.1016/s0246-0203(97)80107-0