Branching diffusion processes and spectral properties of Feynman-Kac semigroup
Résumé
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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