Probabilistic Theory of Mean Field Games with Applications I Mean Field FBSDEs Control and Games 1st Edition René Carmona 3319589202 9783319589206

Probabilistic Theory of Mean Field Games with Applications I Mean Field FBSDEs Control and Games 1st Edition René Carmona – Ebook Instant Download/Delivery ISBN(s): 3319589202, 9783319589206

Product details:

• ISBN 10:  3319589202
• ISBN 13: 9783319589206
• Author:  René Carmona

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 book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach.

Table of contents:

Part I. The Probabilistic Approach to Mean Field Games

1. Learning by Examples: What Is a Mean Field Game?

2. Probabilistic Approach to Stochastic Differential Games

3. Stochastic Differential Mean Field Games

4. FBSDEs and the Solution of MFGs Without Common Noise

Part II. Analysis on Wasserstein Space and Mean Field Control

5. Spaces of Measures and Related Differential Calculus

6. Optimal Control of SDEs of McKean-Vlasov Type

7. Extensions for Volume I

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