Branching diffusion processes and spectral properties of Feynman-Kac semigroup

Pierre Collet; Sylvie Méléard; Jaime San MARTIN

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arXiv · 2404.09568

Branching diffusion processes and spectral properties of Feynman-Kac semigroup

Pierre Collet·Sylvie Méléard·Jaime San MARTIN

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Abstract

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.

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Pierre Collet, Sylvie Méléard, Jaime San MARTIN. 2024-04-15. Branching diffusion processes and spectral properties of Feynman-Kac semigroup. https://arxiv.org/abs/2404.09568

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