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CONDITIONS FOR RECURRENCE AND TRANSIENCE FOR TIME-INHOMOGENEOUS BIRTH-AND-DEATH PROCESSES

Part of: Stochastic processes Markov processes Stochastic analysis

Published online by Cambridge University Press:  23 June 2023

VYACHESLAV M. ABRAMOV Open the ORCID record for VYACHESLAV M. ABRAMOV [Opens in a new window]
VYACHESLAV M. ABRAMOV*
Affiliation:
24 Sagan Drive, Cranbourne North, Victoria 3977, Australia
*
e-mail: vabramov126@gmail.com
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Abstract

We derive 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 [‘Urn-related random walk with drift $\rho x^\alpha /t^\beta $’, Electron. J. Probab. 13 (2008), 944–960] follow.

Keywords

random walksbirth-and-death processesrecurrence and transiencemartingales with continuous parameterstochastic calculus

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G44: Martingales with continuous parameter 60H07: Stochastic calculus of variations and the Malliavin calculus 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 2 , April 2024 , pp. 393 - 402
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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