Revisits for transient random walk

C. C. Heyde

Stochastic Processes and their Applications, 1973, vol. 1, issue 1, 33-51

Abstract: For a random walk on the integers define Rn as the number of (distinct) states visited in the first n steps and Zn as the number of states visited in the first n steps which are never revisited. Here we deal with transient walks. The increments of Zn form a stationary process and various central limit results and an iterated logarithm result are obtained for Zn from known results on stationary processes. Furthermore, the limit behaviour of Rn is closely related to that of Zn; this relationship is elucidated and corresponding limit results for Rn are then read off from those for Zn.

Date: 1973
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