François Delarue - Böcker
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24 produkter
24 produkter
1 527 kr
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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.
692 kr
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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.
Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
Häftad, Engelska, 2023
967 kr
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View the abstract.
1 361 kr
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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.
967 kr
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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
155 kr
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164 kr
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197 kr
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150 kr
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141 kr
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150 kr
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197 kr
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Avis Sur Les Maladies Vénériennes. Description Par Laquelle on Peut Reconnaître Ces Maladies
Moyens Que l'On Peut Employer Pour Se Guérir
Häftad, Franska, 2018
197 kr
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Tableau de la Syphilis, Dite Maladie Vénérienne. 2e Édition
Contenant Les Moyens de Se Préserver Des Suites Fâcheuses de Cette Terrible Maladie
Häftad, Franska, 2018
191 kr
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Cours Complet Des Maladies Des Yeux, Suivi d'Un Traité Abrégé d'Hygiène Oculaire
Häftad, Franska, 2018
387 kr
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155 kr
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137 kr
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Du Pouvoir Constituant Et Du Principe Souverain, d'Après M. de Cormenin
Au Sujet de la Charte de 1830
Häftad, Franska, 2018
126 kr
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224 kr
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Probabilistic Theory of Mean Field Games with Applications II
Mean Field Games with Common Noise and Master Equations
Häftad, Engelska, 2019
1 473 kr
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This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.
Probabilistic Theory of Mean Field Games with Applications I
Mean Field FBSDEs, Control, and Games
Häftad, Engelska, 2019
1 682 kr
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This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications.
402 kr
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This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M.
Probabilistic Theory of Mean Field Games with Applications II
Mean Field Games with Common Noise and Master Equations
Inbunden, Engelska, 2018
1 473 kr
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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
Mean Field FBSDEs, Control, and Games
Inbunden, Engelska, 2018
1 682 kr
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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 resultsto 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.