Ergodic control of McKean-Vlasov SDEs and associated Bellman equation

被引：2

作者：

Bao, Xiaofan ^{[1
]}

Tang, Shanjian ^{[2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Sch Math Sci, Dept Finance & Control Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期

基金：

中国国家自然科学基金;

关键词：

McKean-Vlasov equations; Hamilton-Jacobi-Bellman equations; Viscosity solutions; Ergodic control; MEAN-FIELD GAMES; STOCHASTIC DIFFERENTIAL-EQUATIONS; NONLINEAR 2ND-ORDER EQUATIONS; VISCOSITY SOLUTIONS; INFINITE DIMENSIONS; TIME BEHAVIOR; SPACE; BSDES;

D O I：

10.1016/j.jmaa.2023.127404

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the ergodic control problem for McKean-Vlasov stochastic differential equations and prove the existence and uniqueness of the viscosity solution to the associated fully nonlinear HJB equation in a lifted sense. Furthermore, as the time horizon goes to infinity, we show that the solutions of finite-horizon time-averaging optimal control problems converge to that of the ergodic control problem. Our results require dissipativity conditions and dissipativity-like conditions on distribution variables of both drift and diffusion coefficients.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：28

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