Stroock, Daniel W.; Zheng, Weian Markov chain approximations to symmetric diffusions. (English) Zbl 0885.60065 Ann. Inst. Henri Poincaré, Probab. Stat. 33, No. 5, 619-649 (1997). A Markov chain approximation for diffusions associated to divergence form operators is considered. The present paper aims to the case of generators with nonsmooth coefficients, in which the identification of limits via Dirichlet forms, which is a basic tool for symmetric Markov processes from divergence form operators, is rather hard. A number of delicate estimations is given first, which leads to a discrete setting of the De Giorgi-Moser-Nash theory. Then, a concrete symmetric Markov chain approximation for symmetric diffusions is found. This approximation for diffusions is different from that in D. W. Stroock and S. R. S. Varadhan’s book “Multidimensional diffusion theory” (1979; Zbl 0426.60069), where the approximate Markov chains are time discrete, while in the present paper the approximate Markov chains are discrete in space. Reviewer: Qian Minping (Beijing) Cited in 39 Documents MSC: 60J60 Diffusion processes 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) Keywords:symmetric diffusion; Dirichlet form; De Giorgi-Moser-Nash theory; divergence form operator; Markov chain Citations:Zbl 0426.60069 PDFBibTeX XMLCite \textit{D. W. Stroock} and \textit{W. Zheng}, Ann. Inst. Henri Poincaré, Probab. Stat. 33, No. 5, 619--649 (1997; Zbl 0885.60065) Full Text: DOI Numdam EuDML