Stopped Random Walks pp 1-7 | Cite as

# 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.

## Keywords

Random Walk Limit Theorem Renewal Process Simple Random Walk Renewal Theory## Preview

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