A criterion for linear drift, and the central limit theorem for one- dimensional random walks in a random environment. (English. Russian original) Zbl 0815.60067

Lëtchikov, A. V.

Russ. Acad. Sci., Sb., Math. 79, No. 1, 73-92 (1994); translation from Mat. Sb. 184, No. 5, 85-110 (1993).

Motivated by the work of Ya. G. Sinaj [Theory Probab. Appl. 27, 256-268 (1982); translation from Teor. Veroyatn. Primen. 27, 247-258 (1982; Zbl 0497.60065)] on the limit behaviour of a one-dimensional random walk in a random environment, the paper continues the series of publications on this subject, concentrating on the problem due to H. Kesten (1984): What are the necessary and sufficient conditions for a positive linear drift, in the general case of a one-dimensional random walk in a random environment, and in particular the conditions under which the central limit theorem is applicable? The respective criteria are given and proved for random walks with bounded jumps, in a unit of time, comprising no more than \(L\) steps to the left and \(R\) steps to the right; \(R\), \(L\) being poisitive integers.

Reviewer: P.Garbaczewski (Wrocław)

MSC:

60G50	Sums of independent random variables; random walks
60F05	Central limit and other weak theorems
60J75	Jump processes (MSC2010)

Keywords:

random environment; central limit theorem; random walks with bounded jumps