On the number of times a simple random walk reaches a onnegative height

Abstract

The purpose of this note is to derive distributional properties of the random variable associated with the number of visits to state r r ≥ 0 during the interval [0,n] of a simple random walk. The random walk is defined in the sense of Cox and Miller, allowing for three step-types, arbitrary probabilities for these steps, and arbitrary terminating state after n steps. It is also shown that some well known results can be obtained as specializations of two general Theorems