Journal Articles ESAIM: Proceedings and Surveys Year : 2019

Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean

Abstract

In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is O(1/N + h). We provide numerical experiments confirming this behaviour and showing that it extends to more general mean-field interaction and study the efficiency of the antithetic sampling technique on the same examples.

Dates and versions

hal-01877002 , version 1 (19-09-2018)

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Cite

Oumaima Bencheikh, Benjamin Jourdain. Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean. ESAIM: Proceedings and Surveys, 2019, CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.219-235. ⟨10.1051/proc/201965219⟩. ⟨hal-01877002⟩
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