Generalized gradient structures for measure-valued population dynamics and their large-population limit

Jasper Hoeksema, Oliver Tse (Corresponding author)

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Samenvatting

We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker–Pacala–Dieckmann-Law model. Under the assumption of detailed balance, we provide a rigorous generalized gradient structure, incorporating the fluxes arising from the birth and death of the particles. Moreover, in the large population limit, we show convergence of the forward Kolmogorov equation to a Liouville equation, which is a transport equation associated with the mean-field limit of the underlying process. In addition, we show convergence of the corresponding gradient structures in the sense of Energy-Dissipation Principles, from which we establish a propagation of chaos result for the particle system and derive a generalized gradient-flow formulation for the mean-field limit.

Originele taal-2Engels
Artikelnummer158
Aantal pagina's72
TijdschriftCalculus of Variations and Partial Differential Equations
Volume62
Nummer van het tijdschrift5
DOI's
StatusGepubliceerd - jun. 2023

Financiering

The authors acknowledge support from NWO Vidi grant 016.Vidi.189.102 on “Dynamical-Variational Transport Costs and Application to Variational Evolution”.

FinanciersFinanciernummer
Nederlandse Organisatie voor Wetenschappelijk Onderzoek016

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