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Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States

Author

Listed:
  • Xiaohan Wu

    (Liaocheng University
    Harbin Institute of Technology
    Southern University of Science and Technology)

  • Anyue Chen

    (Southern University of Science and Technology
    University of Liverpool)

  • Junping Li

    (Central South University)

Abstract

Based on the resolvent decomposition theorems presented very recently by Chen (J Theor Probab 33:2089–2118, 2020), in this paper we focus on investigating the fundamental problems of existence and uniqueness criteria for Denumerable Markov Processes with finitely many instantaneous states. Some elegant sufficient and necessary conditions are obtained for this less-investigated topic. A few important examples including the generalized Kolmogorov models are presented to illustrate our general results.

Suggested Citation

  • Xiaohan Wu & Anyue Chen & Junping Li, 2024. "Existence and Uniqueness of Denumerable Markov Processes with Instantaneous States," Journal of Theoretical Probability, Springer, vol. 37(1), pages 511-532, March.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01299-w
    DOI: 10.1007/s10959-023-01299-w
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    References listed on IDEAS

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    1. Chen, Anyue & Renshaw, Eric, 1995. "Markov branching processes regulated by emigration and large immigration," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 339-359, June.
    2. Chen, Anyue & Renshaw, Eric, 1993. "Recurrence of Markov branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 231-242, April.
    3. Anyue Chen, 2020. "Resolvent Decomposition Theorems and Their Application in Denumerable Markov Processes with Instantaneous States," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2089-2118, December.
    4. Chen, Anyue & Renshaw, Eric, 2000. "Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 177-193, August.
    Full references (including those not matched with items on IDEAS)

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