The Rate of Escape of a Polynomial Random Walk on ℕ2

Léonard Gallardo
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Léonard Gallardo: Université de Brest, Départment de Mathématiques

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 233-247 from Springer

Abstract: Abstract The simple random walk S n on ℕ2 associated with the disk polynomials of index α > 0, is a transient process. The purpose of this paper is to prove an integral test that determines for a given sequence u n whether P(|S n |) ≤ u n infinitely often) is 0 or 1. After reduction to a one dimensional problem, we use the potential theory of the Gegenbauer polynomials to achieve a complete solution.

Keywords: Random Walk; Iterate Logarithm; Simple Random Walk; Polynomial Random; Gelfand Pair (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2323-3_19

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DOI: 10.1007/978-1-4899-2323-3_19

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