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Branching diffusion processes and spectral properties of Feynman-Kac semigroup
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In this article we study the long time behavior of linear functionals of branching diffusion processesas well as the time reversal of the spinal process by means of spectral properties of the Feynman-Kacsemigroup. We generalize for this non Markovian semigroup the theory of quasi-stationary distribution(q.s.d.) and Q-process. The most amazing result is the identification of the law of the reversal time spinalprocess issued from q.s.d. with the Q-process of the Feynman-Kac semigroup.
Forward citations
Cited by 3 Pith papers
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Long-Time Behaviors of Branching-Diffusion Processes via Spectral Analysis
Establishes exponential convergence rates for the total mass of branching-diffusion processes and characterizes their quasi-stationary distributions via a novel spectral transformation and heat kernel estimates.
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Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes
For real-trait birth-death processes, the paper proves moment recurrences, extinction-probability asymptotics, and convergence to a Yaglom limit and Q-process when the population is conditioned to survive.
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Long time behavior of killed Feynman-Kac semigroups with singular Schr{\"o}dinger potentials
Establishes compactness and long-time convergence for killed Feynman-Kac semigroups with singular Schrödinger potentials on a broad class of Feller processes from statistical physics.
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