Two-Dimensional Recurrent Random Walk

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


Just about all worthwhile known results concerning random walk (or concerning any stochastic process for that matter) are closely related to some stopping time T as defined in definition D3.3. Thus we plan to investigate stopping times. Given a stopping time T we shall usually be concerned with the random variable x T., the position of the random walk at a random time which depends only on the past of the process. There can be no doubt that problems concerning x T represent a natural generalization of the theory in Chapters I and II; for in those chapters our interest was confined to the iterates P n (0,x) of the transition function—in other words, to the probability law governing x n at an arbitrary but nonrandom time.


Random Walk Time Dependent Behavior Simple Random Walk Harmonic Polynomial Symmetric Random Walk 


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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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