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

Deheuvels, Paul; Révész, Pál

Probab. Theory Relat. Fields 72, 215-230 (1986).

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.

MSC:

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

Keywords:

random walk in a random environment; transience; recurrence; local time; law of the iterated logarithm

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