Existence of quasi-stationary distributions for downward skip-free Markov chains

Kosuke Yamato

Stochastic Processes and their Applications, 2025, vol. 183, issue C

Abstract: For downward skip-free continuous-time Markov chains on non-negative integers killed at zero, the existence of the quasi-stationary distribution is studied. The scale function for the process is introduced, and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller’s classification of the boundary for birth-and-death processes. The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.

Keywords: Downward skip-free Markov chain; Quasi-stationary distribution; Yaglom limit; Scale function; Boundary classification (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104579

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