Summary
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.
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Deheuvels, P., Révész, P. Simple random walk on the line in random environment. Probab. Th. Rel. Fields 72, 215–230 (1986). https://doi.org/10.1007/BF00699104
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DOI: https://doi.org/10.1007/BF00699104
Keywords
- Stochastic Process
- Random Walk
- Probability Theory
- Mathematical Biology
- Simple Proof