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Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games: Probability Theory and Stochastic Modelling, cartea 83

Autor René Carmona, François Delarue
en Limba Engleză Hardback – 12 mar 2018
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.
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Specificații

ISBN-13: 9783319564371
ISBN-10: 3319564374
Pagini: 700
Ilustrații: XXVI, 714 p.
Dimensiuni: 155 x 235 x 49 mm
Greutate: 1.18 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Probability Theory and Stochastic Modelling

Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“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)

Textul de pe ultima copertă

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.

Caracteristici

First comprehensive presentation of state of the art theory of mean field games with special emphasis on the probabilistic approach Numerous applications with explicit examples including numerical solutions Self-contained treatment of related topics such as analysis on Wasserstein space and mean field control problems