Correlated random walks. (English) Zbl 0542.60067

Bender, Edward A.; Richmond, L. Bruce

Ann. Probab. 12, 274-278 (1984).

We consider random walks on lattices with finite memory and a finite number of possible steps. Using a local limit theorem, we generalize Polya’s theorem to such walks, describe how to compute tail probabilities when the number of steps is large, and obtain asymptotic estimates for the average number of points visited.

MSC:

60G50	Sums of independent random variables; random walks
60C05	Combinatorial probability

Keywords:

correlated random walks; random walks on lattices; tail probabilities; asymptotic estimates