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101 0 $aeng
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200 10$aProbabilistic Theory of Mean Field Games with Applications I $eMean Field FBSDEs, Control, and Games /$fby René Carmona, François Delarue
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (728 pages)
225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v83
311   $a3-319-56437-4 
320   $aIncludes bibliographical references and index.
327   $aPreface 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.
330   $aThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
410  0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v83
606   $aProbabilities
606   $aCalculus of variations
606   $aPartial differential equations
606   $aEconomic theory
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$aCalculus of variations.
615  0$aPartial differential equations.
615  0$aEconomic theory.
615 14$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   $a510
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
906   $aBOOK
912   $a9910300125703321
996   $aProbabilistic Theory of Mean Field Games with Applications I$92240084
997   $aUNINA