Carleman Estimates in Mean Field Games
Stability and Uniqueness for Nonlinear PDEs and Inverse Problems
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Carleman Estimates in Mean Field Games
Stability and Uniqueness for Nonlinear PDEs and Inverse Problems
About this book
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.
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Information
Table of contents
- Title Page
- Copyright
- Contents
- Frontmatter
- Dedication
- Contents
- 1 Retrospective problem of mean field games
- 2 Stability and uniqueness for semiforecasting and forecasting problems
- 3 Hölder stability and uniqueness for the case of lateral Cauchy data
- 4 Hölder stability for a coefficient inverse problem for the mean field games system
- 5 Convexification numerical method for the retrospective problem for mean field games
- 6 Convexification for a coefficient inverse problem for mean field games
- Index
- Subject Index