Mean field type models describing the limiting behavior, as the number of players tends to +∞, of stochastic differential game problems, have been recently introduced by J.-M. Lasry and P.-L. Lions [C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 619-625; C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 679-684; Jpn. J. Math., 2 (2007), pp. 229-260]. Numerical methods for the approximation of the stationary and evolutive versions of such models are proposed here. In particular, existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated. Numerical experiments are carried out. © 2010 Society for Industrial and Applied Mathematics.
Mean field games: Numerical methods / CAPUZZO DOLCETTA, Italo; Yves, Achdou. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 48:3(2010), pp. 1136-1162. [10.1137/090758477]
Mean field games: Numerical methods
CAPUZZO DOLCETTA, Italo;
2010
Abstract
Mean field type models describing the limiting behavior, as the number of players tends to +∞, of stochastic differential game problems, have been recently introduced by J.-M. Lasry and P.-L. Lions [C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 619-625; C. R. Math. Acad. Sci. Paris, 343 (2006), pp. 679-684; Jpn. J. Math., 2 (2007), pp. 229-260]. Numerical methods for the approximation of the stationary and evolutive versions of such models are proposed here. In particular, existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated. Numerical experiments are carried out. © 2010 Society for Industrial and Applied Mathematics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
