Abstract:The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' \emph{Bull. Aust. Math. Soc.} \textbf{109} (2024), 393--402] for the case of time-inhomogeneous random walks, the increments of which take values in $\mathbb{R}$. By this, we give a full solution of the open problem formulated by Menshikov and Volkov [`Urn-related random walk with drift $\rho x^\alpha/t^\beta$' \emph{Electron. J. Probab.}, \textbf{13} (2008), paper No. 31, 944--960] that was partially solved in the aforementioned paper by Abramov.
From: Vyacheslav M. Abramov [view email]
[v1]
Mon, 13 Nov 2023 23:14:32 UTC (6 KB)
[v2]
Mon, 27 Nov 2023 03:27:16 UTC (7 KB)
[v3]
Tue, 23 Apr 2024 09:11:33 UTC (8 KB)
[v4]
Fri, 11 Sep 2026 06:22:33 UTC (12 KB)
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