English

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

Probability 2018-04-16 v1

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.

Keywords

Cite

@article{arxiv.1804.04905,
  title  = {On a Feynman-Kac approach to growth-fragmentation semigroups and their asymptotic behaviors},
  author = {Jean Bertoin},
  journal= {arXiv preprint arXiv:1804.04905},
  year   = {2018}
}