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First-passage time for Sinai’s random walk in a random environment

Part of: Stochastic processes Special processes Markov processes

Published online by Cambridge University Press:  29 November 2024

Wenming Hong  and
Mingyang Sun Open the ORCID record for Mingyang Sun [Opens in a new window]
Wenming Hong*
Affiliation:
Beijing Normal University
Mingyang Sun*
Affiliation:
Beijing Normal University
*
*Postal address: School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P.R. China.
*Postal address: School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P.R. China.
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Abstract

We investigate the tail behavior of the first-passage time for Sinai’s random walk in a random environment. Our method relies on the connection between Sinai’s walk and branching processes with immigration in a random environment, and the analysis on some important quantities of these branching processes such as extinction time, maximum population, and total population.

Keywords

First-passage timerandom walkrandom environmentbranching process

MSC classification

Primary: 60K37: Processes in random environments
Secondary: 60G50: Sums of independent random variables; random walks 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 62 , Issue 2 , June 2025 , pp. 756 - 774
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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