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Probabilistic theory of mean field g...

Carmona, Rene.

Probabilistic theory of mean field games with applications.II,Mean field games with common noise and master equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Probabilistic theory of mean field games with applications.by Rene Carmona, Francois Delarue.
其他題名:	Mean field games with common noise and master equations
作者:	Carmona, Rene.
其他作者:	Delarue, Francois.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xxiv, 700 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mean field theory.
電子資源:	http://dx.doi.org/10.1007/978-3-319-56436-4
ISBN:	9783319564364$q(electronic bk.)

Probabilistic theory of mean field games with applications.II,Mean field games with common noise and master equations
Carmona, Rene.

Probabilistic theory of mean field games with applications.II,Mean field games with common noise and master equations[electronic resource] /Mean field games with common noise and master equationsby Rene Carmona, Francois Delarue. - Cham :Springer International Publishing :2018. - xxiv, 700 p. :ill., digital ;24 cm. - Probability theory and stochastic modelling,v.842199-3130 ;. - Probability theory and stochastic modelling ;v.70..

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.

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.

ISBN: 9783319564364$q(electronic bk.)

Standard No.: 10.1007/978-3-319-56436-4doiSubjects--Topical Terms:

262949
Mean field theory.

LC Class. No.: QC174.85.M43 / C376 2018

Dewey Class. No.: 530.144

Probabilistic theory of mean field games with applications.II,Mean field games with common noise and master equations
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505 0 $a 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.
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 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.
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