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

Jean Bertoin

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arXiv · 1804.04905

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

Jean Bertoin

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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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Jean Bertoin. 2018-04-13. On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. https://arxiv.org/abs/1804.04905

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