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- W2981694852 abstract "In this paper, we analyse the rate of convergence of a system of $N$ interacting particles with mean-field rank based interaction in the drift coefficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikhov to check trajectorial propagation of chaos with optimal rate $N^{-1/2}$ to the associated stochastic differential equations nonlinear in the sense of McKean. We next relax the assumptions needed by Bossy to check convergence in $L^1(mathbb{R})$ with rate ${mathcal O}(frac{1}{sqrt N} + h)$ of the empirical cumulative distribution function of the Euler discretization with step $h$ of the particle system to the solution of a one dimensional viscous scalar conservation law. Last, we prove that the bias of this stochastic particle method behaves in ${mathcal O}(frac{1}{N} + h)$. We provide numerical results which confirm our theoretical estimates." @default.
- W2981694852 created "2019-11-01" @default.
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- W2981694852 date "2022-01-01" @default.
- W2981694852 modified "2023-09-27" @default.
- W2981694852 title "Weak and strong error analysis for mean-field rank based particle approximations of one dimensional viscous scalar conservation law" @default.
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