Simple random walk on the line in random environment. (English) Zbl 0572.60070

We obtain strong limiting bounds for the maximal excursion and for the maximum reached by a random walk in a random environment. Our results derive from a simple proof of Pólya’s theorem for the recurrence of the random walk on the line. As applications, we obtain bounds for the number of visits of the random walk at the origin.


60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks
60J55 Local time and additive functionals
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