The Resource Probabilistic Theory of Mean Field Games with Applications I : Mean Field FBSDEs, Control, and Games, by René Carmona, François Delarue, (electronic resource)

Probabilistic Theory of Mean Field Games with Applications I : Mean Field FBSDEs, Control, and Games, by René Carmona, François Delarue, (electronic resource)

Label
Probabilistic Theory of Mean Field Games with Applications I : Mean Field FBSDEs, Control, and Games
Title
Probabilistic Theory of Mean Field Games with Applications I
Title remainder
Mean Field FBSDEs, Control, and Games
Statement of responsibility
by René Carmona, François Delarue
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
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 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
Member of
http://library.link/vocab/creatorName
Carmona, René
Dewey number
510
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • bIXBKNZSgOc
  • zSVvvkzFKLM
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Delarue, François.
Series statement
Probability Theory and Stochastic Modelling,
Series volume
83
http://library.link/vocab/subjectName
  • Distribution (Probability theory
  • Mathematical optimization
  • Differential equations, partial
  • Economic theory
  • Probability Theory and Stochastic Processes
  • Calculus of Variations and Optimal Control; Optimization
  • Partial Differential Equations
  • Economic Theory/Quantitative Economics/Mathematical Methods
Label
Probabilistic Theory of Mean Field Games with Applications I : Mean Field FBSDEs, Control, and Games, by René Carmona, François Delarue, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface 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
Dimensions
unknown
Edition
1st ed. 2018.
Extent
1 online resource (728 pages).
Form of item
online
Isbn
9783319589206
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-58920-6
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)4100000002485284
  • (MiAaPQ)EBC5341346
  • (DE-He213)978-3-319-58920-6
  • (EXLCZ)994100000002485284
Label
Probabilistic Theory of Mean Field Games with Applications I : Mean Field FBSDEs, Control, and Games, by René Carmona, François Delarue, (electronic resource)
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface 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
Dimensions
unknown
Edition
1st ed. 2018.
Extent
1 online resource (728 pages).
Form of item
online
Isbn
9783319589206
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-58920-6
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)4100000002485284
  • (MiAaPQ)EBC5341346
  • (DE-He213)978-3-319-58920-6
  • (EXLCZ)994100000002485284

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