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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2023

Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanisms and related problems

Résumé

Mean-field integro-differential equations are studied in an abstract framework, through couplings of the corresponding stochastic processes. In the perturbative regime, the equation is proven to admit a unique equilibrium, toward which the process converges exponentially fast. Similarly, in this case, the associated particle system is proven to converge toward its equilibrium at a rate independent from the number of particles.
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Dates et versions

hal-04126325 , version 1 (13-06-2023)

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Pierre Monmarché. Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanisms and related problems. ESAIM: Probability and Statistics, 2023, 27, pp.278-323. ⟨10.1051/ps/2023002⟩. ⟨hal-04126325⟩
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