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Distribution of the number of visits of a random walk. (English) Zbl 0930.60039
The present mathematical note considers a simple random walk and associates it to a sequence of excursions. The main result of the paper is to obtain the distribution of the number of visits during a (fixed) excursion of the random walk. This distribution is shown to be a zero-modified geometric law, which is an extension of P. Revesz’s result (1990). The computed distribution can be applied for testing randomness of a sequence of binary bits.

MSC:
60G50 Sums of independent random variables; random walks
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