Probabilistic Theory of Mean Field Games with Applications I Mean Field FBSDEs, Control, and Games /

• Main Authors: Carmona, René (Author, http://id.loc.gov/vocabulary/relators/aut), Delarue, François (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Probability Theory and Stochastic Modelling, 83
• Subjects: Probabilities.; Calculus of variations.; Partial differential equations.; Economic theory.; Probability Theory and Stochastic Processes.; Calculus of Variations and Optimal Control; Optimization.; Partial Differential Equations.; Economic Theory/Quantitative Economics/Mathematical Methods.

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the...

Table of Contents:

• Preface to Volume I
• Part I: The Probabilistic Approach to Mean Field Games
• Learning by Examples: What is a Mean Field Game?
• Probabilistic Approach to Stochastic Differential Games
• Stochastic Differential Mean Field Games
• FBSDEs and the Solution of MFGs without Common Noise
• Part II: Analysis on Wasserstein Space and Mean Field Control
• Spaces of Measures and Related Differential Calculus
• Optimal Control of SDEs of McKean-Vlasov Type
• Epologue to Volume I
• Extensions for Volume I. References
• Indices.