MEAN FIELD GAMES: CONVERGENCE OF A FINITE DIFFERENCE METHOD

被引：63

作者：

Achdou, Yves ^{[1
]}

Camilli, Fabio ^{[2
]}

Capuzzo-Dolcetta, Italo ^{[3
]}

机构：

[1] Univ Paris Diderot, UPMC, CNRS, Lab Jacques Louis Lions,UMR 7598, F-75205 Paris, France

[2] Sapienza Univ Roma, Dipartimento Sci Base Applicate Ingn, I-00161 Rome, Italy

[3] Sapienza Univ Roma, Dipartimento Matemat, I-00185 Rome, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 05期

关键词：

mean field games; finite difference schemes; convergence; NUMERICAL-METHODS; EQUILIBRIA;

D O I：

10.1137/120882421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +infinity have been recently introduced by Lasry and Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works. Here, convergence theorems for these methods are proved under various assumptions on the coupling operator.

引用

页码：2585 / 2612

页数：28

共 23 条

[1] ITERATIVE STRATEGIES FOR SOLVING LINEARIZED DISCRETE MEAN FIELD GAMES SYSTEMS [J].

Achdou, Yves ;

Perez, Victor .

NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (02) :197-217

[2] MEAN FIELD GAMES: NUMERICAL METHODS FOR THE PLANNING PROBLEM [J].

Achdou, Yves ;

Camilli, Fabio ;

Capuzzo-Dolcetta, Italo .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (01) :77-109

[3] MEAN FIELD GAMES: NUMERICAL METHODS [J].

Achdou, Yves ;

Capuzzo-Dolcetta, Italo .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (03) :1136-1162

[4]

Bardi M., 1997, SYSTEMS CONTROL FDN

[5]

BREZIS H, 1983, COLLECTION MATH APPL

[6] A SEMI-DISCRETE APPROXIMATION FOR A FIRST ORDER MEAN FIELD GAME PROBLEM [J].

Camilli, Fabio ;

Silva, Francisco .

NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (02) :263-277

[7]

Cardaliaguet P., 2011, PREPRINT

[8] LONG TIME AVERAGE OF MEAN FIELD GAMES [J].

Cardaliaguet, Pierre ;

Lasry, Jean-Michel ;

Lions, Pierre-Louis ;

Porretta, Alessio .

NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (02) :279-301

[9]

Eymard R, 2000, HDBK NUM AN, V7, P713

[10]

Eymard R, 1998, RAIRO-MATH MODEL NUM, V32, P747

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