LEADER 04467nam 22006375 450 001 9910300116003321 005 20200703105307.0 010 $a3-319-56436-6 024 7 $a10.1007/978-3-319-56436-4 035 $a(CKB)4100000002891982 035 $a(MiAaPQ)EBC5319949 035 $a(DE-He213)978-3-319-56436-4 035 $a(PPN)22555223X 035 $a(EXLCZ)994100000002891982 100 $a20180307d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aProbabilistic Theory of Mean Field Games with Applications II $eMean Field Games with Common Noise and Master Equations /$fby René Carmona, François Delarue 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (697 pages) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v84 311 $a3-319-56435-8 320 $aIncludes bibliographical references and index. 327 $aForeword -- 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. 330 $aThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v84 606 $aProbabilities 606 $aCalculus of variations 606 $aDifferential equations, Partial 606 $aEconomics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 615 0$aProbabilities. 615 0$aCalculus of variations. 615 0$aDifferential equations, Partial. 615 0$aEconomics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aPartial Differential Equations. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 676 $a530.1595 700 $aCarmona$b René$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149642 702 $aDelarue$b François$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300116003321 996 $aProbabilistic Theory of Mean Field Games with Applications II$92272616 997 $aUNINA