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Sharp propagation of chaos for McKean-Vlasov equation with non constant diffusion coefficient
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We present a method to obtain sharp local propagation of chaos results for a system of N particles with a diffusion coefficient that it not constant and may depend of the empirical measure. This extends the recent works of Lacker [14] and Wang [24] to the case of non constant diffusions. The proof relies on the BBGKY hierarchy to obtain a system of differential inequalities on the relative entropy of k particles, involving the fisher information.
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Propagation of chaos and approximation error of random batch particle system in the mean field regime
For the random batch particle system, the k-particle relative entropy to the mean-field limit is bounded by C t e^{C t} (k^2/N^2 + k tau^2).
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