Averaging method and random walks in inhomogeneous environment. (Russian) Zbl 0592.60054

Kozlov, S. M.

Usp. Mat. Nauk 40, No. 2(242), 61-120 (1985).

The paper deals with the asymptotic behavior of a Markov chain on a \(d\)-dimensional lattice with random transition probabilities when the number of steps is large. A central limit theorem is established for many important classes of random walks. The method of averaging developed recently in the theory of partial differential equations is applied. This method yields effective criteria for a central limit theorem in a random nonhomogeneous environment.

Reviewer: L.Kalyakin

MSC:

60G50	Sums of independent random variables; random walks
60F05	Central limit and other weak theorems

Keywords:

lattice with random transition probabilities; central limit theorem; method of averaging; nonhomogeneous environment