MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY

• 成果类型: Article
• 署名作者: Gangbo, Wilfrid; Meszaros, Alpar R.; Mou, Chenchen; Zhang, Jianfeng
• 署名单位: University of California System; University of California Los Angeles; Durham University; City University of Hong Kong; University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1580
• 发表日期: 2022
• 页码: 2178-2217
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS

摘要

In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry-Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.