Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes

2022/12/04 by Vyacheslav M. Abramov, Abramov, Vyacheslav M.
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2212.01722

openalex publication_date 2022/12/04 · openalex created_date 2022/12/18 · openalex updated_date 2026/07/28

Abstract

We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [Electron. J. Probab., 13 (2008), paper No. 31, 944--960] follow.

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