On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors

Abstract : This work develops further a probabilist approach to the asymptotic behavior of growth-fragmentation semigroups via the Feynman-Kac formula, which was introduced in a joint article with A.R. Watson [4]. Here, it is first shown that the sufficient condition for a Malthusian behavior which was established in [4], is also necessary. We then provide a simple criterion to ensure exponential speed of convergence, which enables us to treat cases than were not covered previously in the literature.
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https://hal.archives-ouvertes.fr/hal-01764139
Contributor : Jean Bertoin <>
Submitted on : Thursday, May 23, 2019 - 7:03:11 AM
Last modification on : Tuesday, June 4, 2019 - 1:02:54 AM

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  • HAL Id : hal-01764139, version 2
  • ARXIV : 1804.04905

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Jean Bertoin. On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. 2019. ⟨hal-01764139v2⟩

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