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1 Bulletin of the Polish Academy of Sciences. Mathematics

1 2003

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A note on the central limit theorem for two-fold stochastic random walks in a random environment

Komorowski T., Olla S.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

217-232

We consider a ciass of two-fold stochastic random walks in a random environment. The transition probability is given by an ergodic random field on Z^d with two-fold stochastic realizations. The central limit theorem for this class of random walks has been claimed by Kozlov under certain strong mixing conditions (cf. [4, Theorem 2.3.3, p. 121]). However the statement and the argument used in [4] is not correct, and we provide a counterexample in dimension two (cf. Example 2.3 below). We give a sufficient condition for the walk to satisfy the central limit theorem (see condition (H) below). Then we give some spectral and mixing conditions that imply condition (H).