The Classification of Random Walk

  • Frank Spitzer
Part of the Graduate Texts in Mathematics book series (GTM, volume 34)


The simplest definition of random walk is an analytical one. It has nothing to do with probability theory, except insofar as probabilistic ideas motivate the definition. In other words, probability theory will “lurk in the background” from the very beginning. Nevertheless there is a certain challenge in seeing how far one can go without introducing the formal (and formidable) apparatus of measure theory which constitutes the mathematical language of probability theory. Thus we shall introduce measure theory (in section 3) only when confronted by problems sufficiently complicated that they would sound contrived if expressed as purely analytic problems, i.e., as problems concerning the transition function which we are about to define.


Random Walk Transition Function Simple Random Walk Transient Case Recurrence Behavior 
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Copyright information

© Frank Spitzer 1964

Authors and Affiliations

  • Frank Spitzer
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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