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Preprints, Working Papers, ... Year : 2024

Branching diffusion processes and spectral properties of Feynman-Kac semigroup

Abstract

In this article we study the long time behavior of linear functionals of branching diffusion processes as well as the time reversal of the spinal process by means of spectral properties of the Feynman-Kac semigroup. 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 spinal process issued from q.s.d. with the Q-process of the Feynman-Kac semigroup.
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hal-04544252 , version 1 (12-04-2024)

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  • HAL Id : hal-04544252 , version 1

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Pierre Collet, Sylvie Méléard, Jaime San MARTIN. Branching diffusion processes and spectral properties of Feynman-Kac semigroup. 2024. ⟨hal-04544252⟩
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