Introduction

Abstract

A random walk is a sequence S _n , n ≥ 0 of random variables with independent, identically distributed (i.i.d.) increments X _k , k ≥ 1 and S ₀ = 0. A Bernoulli random walk (also called a Binomial random walk or a Binomial process) is a random walk for which the steps equal 1 or 0 with probabilities p and q, respectively, where 0 < p < 1 and p + q = 1. A simple random walk is a random walk for which the steps equal + 1 or − 1 with probabilities p and q, respectively, where, again, 0 < p < 1 and p + q = 1. The case p = q = ½ is called the symmetric simple random walk (sometimes the coin-tossing random walk or the symmetric Bernoulli random walk). A renewal process is a random walk with nonnegative increments; the Bernoulli random walk is an example of a renewal process.