| Issue |
ESAIM: ProcS
Volume 65, 2019
CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|
|
|---|---|---|
| Page(s) | 219 - 235 | |
| DOI | https://doi.org/10.1051/proc/201965219 | |
| Published online | 02 April 2019 | |
Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
Université Paris-Est, Cermics (ENPC), INRIA, F-77455 Marne-la-Vallé, France
e-mail: oumaima.bencheikh@enpc.fr ; benjamin.jourdain@enpc.fr
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(N-1+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.
© EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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