Principles of Random Walk pp 105-173 | Cite as

# Two-Dimensional Recurrent Random Walk

## Abstract

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.

## Keywords

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

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