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Probabilistic Theory of Mean Field Games with Applications I: Mean Field Fbsdes, Control, and Games
Hardcover
Series: Probability Theory and Stochastic Modelling, Book 83
CalculusGeneral MathematicsProbability & Statistics
ISBN13: 9783319564371
Publisher: Springer Nature
Published: Mar 12 2018
Pages: 714
Weight: 2.60
Height: 1.63 Width: 6.52 Depth: 9.36
Language: English
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 results to 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.
3 different editions
Also available
Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations
Carmona, René
Delarue, François
Paperback
Probabilistic Theory of Mean Field Games with Applications I: Mean Field Fbsdes, Control, and Games
Carmona, René
Delarue, François
Paperback
Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations
Delarue, François
Carmona, René
Hardcover
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