The Master Equation And The Convergence Problem In Mean Field Games
DOWNLOAD
Download The Master Equation And The Convergence Problem In Mean Field Games PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Master Equation And The Convergence Problem In Mean Field Games book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Master Equation And The Convergence Problem In Mean Field Games
DOWNLOAD
Author : Pierre Cardaliaguet
language : en
Publisher: Princeton University Press
Release Date : 2019-08-13
The Master Equation And The Convergence Problem In Mean Field Games written by Pierre Cardaliaguet and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-13 with Mathematics categories.
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
The Master Equation And The Convergence Problem In Mean Field Games
DOWNLOAD
Author : Pierre Cardaliaguet
language : en
Publisher: Princeton University Press
Release Date : 2019-08-13
The Master Equation And The Convergence Problem In Mean Field Games written by Pierre Cardaliaguet and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-13 with Mathematics categories.
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Mean Field Games
DOWNLOAD
Author : Yves Achdou
language : en
Publisher: Springer Nature
Release Date : 2021-01-19
Mean Field Games written by Yves Achdou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Mathematics categories.
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Mean Field Games
DOWNLOAD
Author : François Delarue
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-14
Mean Field Games written by François Delarue and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
A Probabilistic Approach To Classical Solutions Of The Master Equation For Large Population Equilibria
DOWNLOAD
Author : Jean-François Chassagneux
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10
A Probabilistic Approach To Classical Solutions Of The Master Equation For Large Population Equilibria written by Jean-François Chassagneux and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.
View the abstract.
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data
DOWNLOAD
Author : Chenchen Mou
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data written by Chenchen Mou and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-13 with Mathematics categories.
View the abstract.
Probabilistic Theory Of Mean Field Games With Applications Ii
DOWNLOAD
Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-08
Probabilistic Theory Of Mean Field Games With Applications Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Mathematics categories.
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.
Probabilistic Theory Of Mean Field Games With Applications I
DOWNLOAD
Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01
Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.
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.
Contemporary Research In Elliptic Pdes And Related Topics
DOWNLOAD
Author : Serena Dipierro
language : en
Publisher: Springer
Release Date : 2019-07-12
Contemporary Research In Elliptic Pdes And Related Topics written by Serena Dipierro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Mathematics categories.
This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Controlo 2024
DOWNLOAD
Author : Antonio Pedro Aguiar
language : en
Publisher: Springer Nature
Release Date : 2025-04-22
Controlo 2024 written by Antonio Pedro Aguiar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-22 with Technology & Engineering categories.
This book offers a perfect insight of the latest research and developments in the fields of dynamic systems and control engineering. Gathering the proceedings of the 16th APCA International Conference on Automatic Control and Soft Computing (CONTROLO 2024), held on July 17-19, 2024, in Porto, Portugal, this volume covers a wide range of theoretical and practical issues relating to the development and use of different control approaches, such as PID control, adaptive control, non-linear control, intelligent monitoring and control based on fuzzy and neural systems. Further topics include robust control systems, and real time control. Sensors and actuators, measurement systems, renewable energy systems, aeronautic and aerospace systems, as well as industrial control and automation, are also comprehensively covered. All in all, this book offers a timely and thoroughly survey of the latest research in the fields of dynamic systems and automatic control engineering, and a source of inspiration for researchers and professionals worldwide.