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 II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players.

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

Inhaltsverzeichnis

Foreword.- Preface to Volume II.- Part I: MFGs with a Common Noise.- Optimization in a Random Environment.- MFGs with a Common Noise: Strong and Weak Solutions.- Solving MFGs with a Common Noise.- Part II: The Master Equation, Convergence, and Approximation Problems.- The Master Field and the Master Equation.- Classical Solutions to the Master Equation.- Convergence and Approximations.- Epilogue to Volume II.- Extensions for Volume II.- References.- Indices.

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xxiv 700 S.
ISBN-13:	9783319564357
ISBN-10:	3319564358
Sprache:	Englisch
Herstellernummer:	978-3-319-56435-7
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:	20.03.2018
Gewicht:	1,238 kg