Approximation of birth–death processes

Liping Li

Stochastic Processes and their Applications, 2025, vol. 190, issue C

Abstract: A birth–death process is a special type of continuous-time Markov chains with minimal state space N. Its resolvent matrix can be fully characterized by a set of parameters (γ,β,ν), where γ and β are non-negative constants, and ν is a positive measure on N. By employing the Ray-Knight compactification, the birth–death process can be realized as a càdlàg process with strong Markov property on the one-point compactification space N¯∂, which includes an additional cemetery point ∂. In a certain sense, the three parameters that determine the birth–death process correspond to its killing, reflecting, and jumping behaviors at ∞ used for the one-point compactification, respectively.

Keywords: Birth-death processes; Continuous-time Markov chains; Ray–Knight compactification; Boundary conditions; Weak convergence; Skorohod topology; Skorohod representation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104756

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