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Probabilistic theory of mean field g...

Carmona, Rene.

Probabilistic theory of mean field games with applications.I,Mean field FBSDEs, control, and games

Record Type:	Electronic resources : Monograph/item
Title/Author:	Probabilistic theory of mean field games with applications.by Rene Carmona, Francois Delarue.
remainder title:	Mean field FBSDEs, control, and games
Author:	Carmona, Rene.
other author:	Delarue, Francois.
Published:	Cham :Springer International Publishing :2018.
Description:	xxvi, 714 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mean field theory.
Online resource:	https://doi.org/10.1007/978-3-319-58920-6
ISBN:	9783319589206$q(electronic bk.)

Probabilistic theory of mean field games with applications.I,Mean field FBSDEs, control, and games
Carmona, Rene.

Probabilistic theory of mean field games with applications.I,Mean field FBSDEs, control, and games[electronic resource] /Mean field FBSDEs, control, and gamesby Rene Carmona, Francois Delarue. - Cham :Springer International Publishing :2018. - xxvi, 714 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.832199-3130 ;. - Probability theory and stochastic modelling ;v.70..

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.

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.

ISBN: 9783319589206$q(electronic bk.)

Standard No.: 10.1007/978-3-319-58920-6doiSubjects--Topical Terms:

262949
Mean field theory.

LC Class. No.: QC174.85.M43 / C37 2018

Dewey Class. No.: 530.144

Probabilistic theory of mean field games with applications.I,Mean field FBSDEs, control, and games
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505 0 $a 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.
520 $a 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.
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