Carleman Estimates in Mean Field Games von Michael V. Klibanov | Stability and Uniqueness for Nonlinear PDEs and Inverse Problems | ISBN 9783111722511

Carleman Estimates in Mean Field Games

Stability and Uniqueness for Nonlinear PDEs and Inverse Problems

von Michael V. Klibanov und Jingzhi Li
Mitwirkende
Autor / AutorinMichael V. Klibanov
Autor / AutorinJingzhi Li
Buchcover Carleman Estimates in Mean Field Games | Michael V. Klibanov | EAN 9783111722511 | ISBN 3-11-172251-1 | ISBN 978-3-11-172251-1

Carleman Estimates in Mean Field Games

Stability and Uniqueness for Nonlinear PDEs and Inverse Problems

von Michael V. Klibanov und Jingzhi Li
Mitwirkende
Autor / AutorinMichael V. Klibanov
Autor / AutorinJingzhi Li

This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields.

This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.