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

2018/04/11 by Jean Bertoin, Bertoin, Jean · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1804.04905

openalex publication_date 2018/04/11 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This work develops further a probabilist approach to the asymptotic behavior\nof growth-fragmentation semigroups via the Feynman-Kac formula, which was\nintroduced in a joint article with A.R. Watson [4]. Here, it is first shown\nthat the sufficient condition for a Malthusian behavior which was established\nin [4], is also necessary. We then provide a simple criterion to ensure\nexponential speed of convergence, which enables us to treat cases than were not\ncovered previously in the literature.\n

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