Probabilistic Theory of Mean Field Games w...

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xxvi 714 S.
ISBN-13:	9783319564371
ISBN-10:	3319564374
Sprache:	Englisch
Herstellernummer:	978-3-319-56437-1
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Delarue, François Carmona, René
Auflage:	1st ed. 2018
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Probability Theory and Stochastic Modelling
Maße:	241 x 160 x 45 mm
Von/Mit:	François Delarue (u. a.)
Erscheinungsdatum:	12.03.2018
Gewicht:	1,262 kg