ON MEAN FIELD SYSTEMS WITH MULTI-CLASSES

被引：4

作者：

Dung Tien Nguyen ^{[1
]}

Son Luu Nguyen ^{[2
]}

Nguyen Huu Du ^{[3
]}

机构：

[1] Vietnam Natl Univ Ho Chi Minh City, Ho Chi Minh City Univ Technol, Fac Appl Sci, Dept Appl Math, 268 Ly Thuong Kiet,Dist 10, Ho Chi Minh City, Vietnam

[2] Univ Puerto Rico, Dept Math, Rio Piedras Campus, San Juan, PR 00925 USA

[3] Hanoi Natl Univ, Dept Math Mech & Informat, 334 Nguyen Trai, Hanoi, Vietnam

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 02期

关键词：

Mean-field model; stochastic differential equation; McKean-Vlasov equation; Monge-Wasserstein distance; multi-classes; MCKEAN-VLASOV LIMIT; GAMES; MODEL; CONVERGENCE;

D O I：

10.3934/dcds.2020057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work focuses on stochastic systems of weakly interacting particles containing different populations represented by multi-classes. The dynamics of each particle depends not only on the empirical measure of the whole population but also on those of different populations. The limits of such systems as the number of particles tends to infinity are investigated. We establish the existence, uniqueness, and basic properties of solutions to the limiting McKean-Vlasov equations of these systems and then obtain the rate of convergence of the sequences of empirical measures associated with the systems to their limits in terms of the pth Monge-Wasserstein distance.

引用

页码：683 / 707

页数：25

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