NUMERICAL METHOD FOR FBSDES OF MCKEAN-VLASOV TYPE

被引：34

作者：

Chassagneux, Jean-Francois ^{[1
]}

Crisan, Dan ^{[2
]}

Delarue, Francois ^{[3
]}

机构：

[1] Univ Paris Diderot, Lab Probabilites Stat & Modelisat, Paris, France

[2] Imperial Coll London, Dept Math, London SW7 2AZ, England

[3] Univ Nice Sophia Antipolis, Lab Jean Alexandre Dieudonne, 28 Ave Valrose, F-06100 Nice, France

来源：

ANNALS OF APPLIED PROBABILITY | 2019年 / 29卷 / 03期

关键词：

McKean-Vlasov; master equation; forward-backward SDE; mean field games; numerical approximation; MEAN-FIELD GAMES; STOCHASTIC DIFFERENTIAL-EQUATIONS; CONVERGENCE; ALGORITHM;

D O I：

10.1214/18-AAP1429

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward- backward systems fail. The scheme is based on a variation of the method of continuation. The principle is to implement recursively local Picard iterations on small time intervals. We establish a bound for the rate of convergence under the assumption that the decoupling field of the forward-backward SDE (or equivalently the solution of the PDE) satisfies mild regularity conditions. We also provide numerical illustrations.

引用

页码：1640 / 1684

页数：45

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