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

DOI10.1016/j.jfa.2019.06.012zbMath1433.35414arXiv1804.04905OpenAlexW2963741941WikidataQ127657726 ScholiaQ127657726MaRDI QIDQ2326492

Jean Bertoin

Publication date: 7 October 2019

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.04905

zbMATH Keywords

Feynman-Kac formulaexponential ergodicitygrowth-fragmentation equationMalthus exponent

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Asymptotic behavior of solutions to PDEs (35B40) One-parameter semigroups and linear evolution equations (47D06) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Ergodic theorems, spectral theory, Markov operators (37A30) Martingales and classical analysis (60G46) Integro-partial differential equations (35R09)

Related Items (13)

Periodic asymptotic dynamics of the measure solutions to an equal mitosis equation ⋮ Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes ⋮ Practical criteria for \(R\)-positive recurrence of unbounded semigroups ⋮ Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate ⋮ Modelling physiologically structured populations: renewal equations and partial differential equations ⋮ A non‐conservative Harris ergodic theorem ⋮ Probabilistic representations of fragmentation equations ⋮ The strong Malthusian behavior of growth-fragmentation processes ⋮ Stochastic methods for the neutron transport equation. I: Linear semigroup asymptotics ⋮ Spectral Gap for the Growth-Fragmentation Equation via Harris's Theorem ⋮ On a family of critical growth-fragmentation semigroups and refracted Lévy processes ⋮ Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process ⋮ A probabilistic view on the long-time behaviour of growth-fragmentation semigroups with bounded fragmentation rates

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