Ray–Knight compactification of birth and death processes

Liping Li

Stochastic Processes and their Applications, 2024, vol. 177, issue C

Abstract: A birth and death process is a continuous-time Markov chain with minimal state space N, whose transition matrix is standard and whose density matrix is a birth–death matrix. Birth and death process is unique if and only if ∞ is an entrance or natural. When ∞ is neither an entrance nor natural, there are two ways in the literature to obtain all birth and death processes. The first one is an analytic treatment proposed by Feller in 1959, and the second one is a probabilistic construction completed by Wang in 1958.

Keywords: Birth and death processes; Continuous-time Markov chains; Ray–Knight compactification; Ray processes; Doob processes; Feller processes; Dirichlet forms; Boundary conditions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104456

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