國立虎尾科技大學 |

Probabilistic Theory of Mean Field Games with Applications II = Mean Field Games with Common Noise and Master Equations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Probabilistic Theory of Mean Field Games with Applications II/ by René Carmona, François Delarue.
Reminder of title:	Mean Field Games with Common Noise and Master Equations /
Author:	Carmona, René.
other author:	Delarue, François.
Description:	XXIV, 700 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1007/978-3-319-56436-4
ISBN:	9783319564364

Probabilistic Theory of Mean Field Games with Applications II = Mean Field Games with Common Noise and Master Equations /
Carmona, René.

Probabilistic Theory of Mean Field Games with Applications IIMean Field Games with Common Noise and Master Equations /[electronic resource] :by René Carmona, François Delarue. - 1st ed. 2018. - XXIV, 700 p.online resource. - Probability Theory and Stochastic Modelling,842199-3130 ;. - Probability Theory and Stochastic Modelling,76.

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

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

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Probabilistic Theory of Mean Field Games with Applications II = Mean Field Games with Common Noise and Master Equations /
LDR:03338nam a22004335i 4500 001 987249
003 DE-He213
005 20200703105307.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319564364 $9 978-3-319-56436-4
024 7 $a 10.1007/978-3-319-56436-4 $2 doi
035 $a 978-3-319-56436-4
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Carmona, René. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1279744
245 1 0 $a Probabilistic Theory of Mean Field Games with Applications II $h [electronic resource] : $b Mean Field Games with Common Noise and Master Equations / $c by René Carmona, François Delarue.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XXIV, 700 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 84
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.
650 0 $a Probabilities. $3 527847
650 0 $a Calculus of variations. $3 527927
650 0 $a Partial differential equations. $3 1102982
650 0 $a Economic theory. $3 809881
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Economic Theory/Quantitative Economics/Mathematical Methods. $3 1069071
700 1 $a Delarue, François. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1279745
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319564357
776 0 8 $i Printed edition: $z 9783319589190
776 0 8 $i Printed edition: $z 9783030132590
830 0 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 76 $3 1254049
856 4 0 $u https://doi.org/10.1007/978-3-319-56436-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)