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Pré-Publication, Document De Travail Année : 2024

Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models

Résumé

The aim of the paper is to prove that the rates of convergence in distribution for $N$-particle mean-field models are the expected one: $N^{-1}$ in Law of Large Numbers regime, and $N^{-1/2}$ in Central Limit Theorem regime. These proofs require to study empirical measures of McKean-Vlasov particle systems, and conditional laws of McKean-Vlasov processes, as measure-valued Markov processes. In particular, the expressions of the infinitesimal generators of such processes are established for measure-valued processes with general jumps. The generators being differential operators, all the proofs rely on the analytical properties of measure-variable functions, and the differentiation of such functions.
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Dates et versions

hal-04505325 , version 1 (14-03-2024)
hal-04505325 , version 2 (21-03-2024)

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  • HAL Id : hal-04505325 , version 2

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Xavier Erny. Study of measure-valued Markov processes. Explicit bounds for the convergence in distribution of mean-field models. 2024. ⟨hal-04505325v2⟩
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