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

Jean Bertoin (1)

1 UZH - Universität Zürich [Zürich] = University of Zurich

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.

Mots clés: Growth-fragmentation equation; Feynman–Kac formula; Malthus exponent; Krein-; Rutman theorem; exponential ergodicity; 2010 Mathematics Subject Classification: 35Q92; 37A30; 47D06; 60G46; 60J25

Domaines: Probabilités [math.PR]

Jean Bertoin. On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors. 2018. ⟨hal-01764139v1⟩