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

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  • Yamato, Kosuke

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.

Suggested Citation

  • Yamato, Kosuke, 2025. "Existence of quasi-stationary distributions for downward skip-free Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000201
    DOI: 10.1016/j.spa.2025.104579
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