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Probabilistic Theory of Mean Field Games with Applications I Rene Carmona

Probabilistic Theory of Mean Field Games with Applications I By Rene Carmona

Probabilistic Theory of Mean Field Games with Applications I by Rene Carmona


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Summary

This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.

Probabilistic Theory of Mean Field Games with Applications I Summary

Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games by Rene 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. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its resultsto the analysis of stochastic mean field control problems.

Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Probabilistic Theory of Mean Field Games with Applications I Reviews

The text is very well-written and can be used to study the theory on various levels. It develops systematically from the wealth of motivating examples and heuristical considerations, through the carefully chosen collection of in-depth explained preliminaries, to the extensive nontrivial theory explained in full detail. The book is highly recommended for those interested in the foundations and the up-to-date development of MFGs, as well as in the general area of stochastic control and related issues of analysis and probability. (Vassili, Mathematical Reviews, January, 2019)

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.

Additional information

NPB9783319564371
9783319564371
3319564374
Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games by Rene Carmona
New
Hardback
Springer International Publishing AG
2018-03-12
714
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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