## The Annals of Probability

- Ann. Probab.
- Volume 12, Number 1 (1984), 274-278.

### Correlated Random Walks

Edward A. Bender and L. Bruce Richmond

#### Abstract

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.

#### Article information

**Source**

Ann. Probab., Volume 12, Number 1 (1984), 274-278.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993392

**Digital Object Identifier**

doi:10.1214/aop/1176993392

**Mathematical Reviews number (MathSciNet)**

MR723748

**Zentralblatt MATH identifier**

0542.60067

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J15

Secondary: 60C05: Combinatorial probability

**Keywords**

Correlated random walks lattices tail probabilities asymptotic estimates

#### Citation

Bender, Edward A.; Richmond, L. Bruce. Correlated Random Walks. Ann. Probab. 12 (1984), no. 1, 274--278. doi:10.1214/aop/1176993392. https://projecteuclid.org/euclid.aop/1176993392