Geodesic
Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
O. Bencheikh1 ; B. Jourdain1
1 Université Paris-Est, Cermics (ENPC), INRIA, F-77455 Marne-la-Vallé, France
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.
DOI : 10.1051/proc/201965219

O. Bencheikh 1 ; B. Jourdain 1

1 Université Paris-Est, Cermics (ENPC), INRIA, F-77455 Marne-la-Vallé, France 
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     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},
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     doi = {10.1051/proc/201965219},
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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965219/

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