Urn-related random walk with drift ρx^α / t^β

2007/11/15 by Mikhail Menshikov, Menshikov, Mikhail, Stanislav Volkov +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G20 #60K35 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G20 #msc:60K35

paper · pdf · doi:10.48550/arxiv.0711.2373

23 pages

arxiv created 2007/11/15 · openalex publication_date 2007/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the walk, and show some interesting applications to Friedman's urn, as well as showing the connection with Lamperti's walk with asymptotically zero drift.

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