Rate of propagation of chaos for diffusive stochastic particle systems via Girsanov transformation
arxiv(2019)
摘要
This paper focus on investigating the explicit rate of convergence for the propagation of chaos, in a pathwise sense a family of interacting stochastic particle related to some Brownian driven McKean-Vlasov dynamics. Precisely the McKean form of nonlinearity is concentrated on a path dependent drift component and satisfies a particular sub-gaussian moment control. Such control enables to derive a uniform estimate of the cost in terms of exponential martingale between the particle and its McKean/mean-field limit system which in turn provide an optimal rate of propagation of chaos in terms of the total variation distance. As a by-product, we deepen some recent propagation of chaos results due to Lacker 2018 and provides a partial stochastic interpretation of the entropy control technique introduced in Jabin and Wang 2016.
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