Two-Dimensional Recurrent Random Walk
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.
KeywordsRandom Walk Time Dependent Behavior Simple Random Walk Harmonic Polynomial Symmetric Random Walk
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