Conditions for recurrence and transience for time-inhomogeneous random walks

2023/11/13 by Vyacheslav M. Abramov, Abramov, Vyacheslav M.
Mathematics · Decision Sciences · #Stochastic processes and statistical mechanics #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2311.07796

Abstract

The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' Bull. Aust. Math. Soc. 109 (2024), 393--402] for the case of time-inhomogeneous random walks, the increments of which take values in ℝ. By this, we give a full solution of the open problem formulated by Menshikov and Volkov [`Urn-related random walk with drift ρx^α/t^β' Electron. J. Probab., 13 (2008), paper No. 31, 944--960] that was partially solved in the aforementioned paper by Abramov.

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