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Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process

Author

Listed:
  • Michel Benaïm

    (Université de Neuchâtel)

  • Nicolas Champagnat

    (Université de Lorraine, CNRS, Inria, IECL)

  • William Oçafrain

    (Université de Lorraine, CNRS, Inria, IECL)

  • Denis Villemonais

    (Université de Lorraine, CNRS, Inria, IECL)

Abstract

In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a transcritical bifurcation. Our proofs are based on the description of the set of quasi-stationary distributions for general two-clusters reducible processes.

Suggested Citation

  • Michel Benaïm & Nicolas Champagnat & William Oçafrain & Denis Villemonais, 2023. "Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1555-1571, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01216-7
    DOI: 10.1007/s10959-022-01216-7
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    References listed on IDEAS

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    1. Hening, Alexandru & Kolb, Martin, 2019. "Quasistationary distributions for one-dimensional diffusions with singular boundary points," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1659-1696.
    2. Champagnat, Nicolas & Villemonais, Denis, 2021. "Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 51-74.
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    Cited by:

    1. Castro, Matheus M. & Lamb, Jeroen S.W. & Olicón-Méndez, Guillermo & Rasmussen, Martin, 2024. "Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: A Banach lattice approach," Stochastic Processes and their Applications, Elsevier, vol. 173(C).

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