Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
ESAIM. Proceedings, Tome 65 (2019), pp. 219-235
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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.
@article{EP_2019_65_a9,
author = {O. Bencheikh and B. Jourdain},
title = {Bias behaviour and antithetic sampling in mean-field particle approximations of {SDEs} nonlinear in the sense of {McKean}},
journal = {ESAIM. Proceedings},
pages = {219--235},
year = {2019},
volume = {65},
doi = {10.1051/proc/201965219},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965219/}
}
TY - JOUR AU - O. Bencheikh AU - B. Jourdain TI - Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean JO - ESAIM. Proceedings PY - 2019 SP - 219 EP - 235 VL - 65 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965219/ DO - 10.1051/proc/201965219 LA - en ID - EP_2019_65_a9 ER -
%0 Journal Article %A O. Bencheikh %A B. Jourdain %T Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean %J ESAIM. Proceedings %D 2019 %P 219-235 %V 65 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965219/ %R 10.1051/proc/201965219 %G en %F EP_2019_65_a9
O. Bencheikh; B. Jourdain. Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean. ESAIM. Proceedings, Tome 65 (2019), pp. 219-235. doi: 10.1051/proc/201965219
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