Transcritical Bifurcation for the Conditional Distribution of a Diffusion Process

Michel Benaïm (), Nicolas Champagnat (), William Oçafrain () and Denis Villemonais ()
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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

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1555-1571

Abstract: 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.

Keywords: Absorbed Markov processes; Quasi-stationary distributions; Exponential mixing; Stochastic differential equations; Bifurcation; 60J25; 60J60; 60B10; 37A25 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-022-01216-7

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