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Introduction

  • Allan Gut
Part of the Applied Probability book series (APPLIEDPROB, volume 5)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • Allan Gut
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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