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Probabilistic Theory of Mean Field Games with Applications I - Mean Field FBSDEs, Control, and Games (Hardcover, 1st ed. 2018):... Probabilistic Theory of Mean Field Games with Applications I - Mean Field FBSDEs, Control, and Games (Hardcover, 1st ed. 2018)
Rene Carmona, Francois Delarue
R4,638 Discovery Miles 46 380 Ships in 12 - 19 working days

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.

Probabilistic Theory of Mean Field Games with Applications II - Mean Field Games with Common Noise and Master Equations... Probabilistic Theory of Mean Field Games with Applications II - Mean Field Games with Common Noise and Master Equations (Hardcover, 1st ed. 2018)
Rene Carmona, Francois Delarue
R3,988 Discovery Miles 39 880 Ships in 10 - 15 working days

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.

Mean Field Games (Paperback): Francois Delarue Mean Field Games (Paperback)
Francois Delarue
R3,105 Discovery Miles 31 050 Ships in 12 - 19 working days

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.

Probabilistic Theory of Mean Field Games with Applications II - Mean Field Games with Common Noise and Master Equations... Probabilistic Theory of Mean Field Games with Applications II - Mean Field Games with Common Noise and Master Equations (Paperback, Softcover reprint of the original 1st ed. 2018)
Rene Carmona, Francois Delarue
R3,958 Discovery Miles 39 580 Ships in 10 - 15 working days

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 (Paperback, Softcover... Probabilistic Theory of Mean Field Games with Applications I - Mean Field FBSDEs, Control, and Games (Paperback, Softcover reprint of the original 1st ed. 2018)
Rene Carmona, Francois Delarue
R3,994 Discovery Miles 39 940 Ships in 9 - 17 working days

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.

Mean Field Games - Cetraro, Italy 2019 (Paperback, 1st ed. 2020): Yves Achdou, Pierre Cardaliaguet, Francois Delarue, Alessio... Mean Field Games - Cetraro, Italy 2019 (Paperback, 1st ed. 2020)
Yves Achdou, Pierre Cardaliaguet, Francois Delarue, Alessio Porretta, Filippo Santambrogio; Edited by …
R1,898 Discovery Miles 18 980 Ships in 10 - 15 working days

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. Lauriere), 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.

A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (Paperback):... A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria (Paperback)
Jean-Francois Chassagneux, Dan Crisan, Francois Delarue
R2,246 Discovery Miles 22 460 Ships in 12 - 19 working days

View the abstract.

The Master Equation and the Convergence Problem in Mean Field Games - (AMS-201) (Paperback): Pierre Cardaliaguet, Francois... The Master Equation and the Convergence Problem in Mean Field Games - (AMS-201) (Paperback)
Pierre Cardaliaguet, Francois Delarue, Jean-Michel Lasry, Pierre-Louis Lions
R2,311 Discovery Miles 23 110 Ships in 10 - 15 working days

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 - (AMS-201) (Hardcover): Pierre Cardaliaguet, Francois... The Master Equation and the Convergence Problem in Mean Field Games - (AMS-201) (Hardcover)
Pierre Cardaliaguet, Francois Delarue, Jean-Michel Lasry, Pierre-Louis Lions
R3,951 R3,645 Discovery Miles 36 450 Save R306 (8%) Ships in 12 - 19 working days

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.

Catalogue de Fonds Et d'Assortiment de Francois Delarue, Editeur d'Estampes (French, Paperback): Francois Delarue Catalogue de Fonds Et d'Assortiment de Francois Delarue, Editeur d'Estampes (French, Paperback)
Francois Delarue
R490 Discovery Miles 4 900 Ships in 10 - 15 working days
Du Pouvoir Constituant Et Du Principe Souverain, d'Apres M. de Cormenin - Au Sujet de la Charte de 1830 (French,... Du Pouvoir Constituant Et Du Principe Souverain, d'Apres M. de Cormenin - Au Sujet de la Charte de 1830 (French, Paperback)
Francois Delarue
R325 Discovery Miles 3 250 Ships in 10 - 15 working days
Memoire Sur Le Croup (French, Paperback): Francois Delarue Memoire Sur Le Croup (French, Paperback)
Francois Delarue
R357 Discovery Miles 3 570 Ships in 10 - 15 working days
Tableau de la Syphilis, Dite Maladie Venerienne. 2e Edition - Contenant Les Moyens de Se Preserver Des Suites Facheuses de... Tableau de la Syphilis, Dite Maladie Venerienne. 2e Edition - Contenant Les Moyens de Se Preserver Des Suites Facheuses de Cette Terrible Maladie (French, Paperback)
Francois Delarue
R489 Discovery Miles 4 890 Ships in 10 - 15 working days
Memoire Sur Les Bons Effets Des Attouchements Avec La Pierre Infernale, Aides d'Une Compression - Methodique Et... Memoire Sur Les Bons Effets Des Attouchements Avec La Pierre Infernale, Aides d'Une Compression - Methodique Et l'Usage Des Collyres Astringens, Traitement Du Straphylome de la Cornee Transparente (French, Paperback)
Francois Delarue
R325 Discovery Miles 3 250 Ships in 10 - 15 working days
Cours Complet Des Maladies Des Yeux, Suivi d'Un Traite Abrege d'Hygiene Oculaire (French, Paperback): Francois Delarue Cours Complet Des Maladies Des Yeux, Suivi d'Un Traite Abrege d'Hygiene Oculaire (French, Paperback)
Francois Delarue
R962 Discovery Miles 9 620 Ships in 10 - 15 working days
Le Vade-Mecum de Chaque Complexion Pour Prolonger La Vie Ou Tableau Raisonne Des Divers Temperamens - Et Des Maladies... Le Vade-Mecum de Chaque Complexion Pour Prolonger La Vie Ou Tableau Raisonne Des Divers Temperamens - Et Des Maladies Occasionnees Par Le Sang, La Bile, La Pituite, Les Glaires, Les Humeurs Noires (French, Paperback)
Francois Delarue
R544 Discovery Miles 5 440 Ships in 10 - 15 working days
Avis Sur Les Maladies Veneriennes. Description Par Laquelle on Peut Reconnaitre Ces Maladies - Moyens Que l'On Peut... Avis Sur Les Maladies Veneriennes. Description Par Laquelle on Peut Reconnaitre Ces Maladies - Moyens Que l'On Peut Employer Pour Se Guerir (French, Paperback)
Francois Delarue
R494 Discovery Miles 4 940 Ships in 10 - 15 working days
Quelques Chapitres Des " Miserables " de Victor Hugo Travestis En Vers Burlesques (French, Paperback): Guillaume-Francois... Quelques Chapitres Des " Miserables " de Victor Hugo Travestis En Vers Burlesques (French, Paperback)
Guillaume-Francois Delarue
R517 Discovery Miles 5 170 Ships in 10 - 15 working days
Recherche de la Verite, Ou Coup d'Oeil Sur La Brochure de M. Le Duc de Rovigo (French, Paperback): Francois Delarue Recherche de la Verite, Ou Coup d'Oeil Sur La Brochure de M. Le Duc de Rovigo (French, Paperback)
Francois Delarue
R353 Discovery Miles 3 530 Ships in 10 - 15 working days
de la Peur Et de la Folie Des Gouvernemens de l'Europe Au Sujet Du Cholera (French, Paperback): Francois Delarue de la Peur Et de la Folie Des Gouvernemens de l'Europe Au Sujet Du Cholera (French, Paperback)
Francois Delarue
R355 Discovery Miles 3 550 Ships in 10 - 15 working days
de la Septennalite Et de Ses Consequences (French, Paperback): Francois Delarue de la Septennalite Et de Ses Consequences (French, Paperback)
Francois Delarue
R389 Discovery Miles 3 890 Ships in 10 - 15 working days
Catalogue de Fonds Et d'Assortiment de Francois Delarue, Editeur d'Estampes... (French, Paperback): Francois Delarue Catalogue de Fonds Et d'Assortiment de Francois Delarue, Editeur d'Estampes... (French, Paperback)
Francois Delarue
R491 Discovery Miles 4 910 Ships in 10 - 15 working days
Cinquieme Supplement Au Catalogue de Fonds Et d'Assortiment: Janvier 1866 (French, Paperback): Francois Delarue Cinquieme Supplement Au Catalogue de Fonds Et d'Assortiment: Janvier 1866 (French, Paperback)
Francois Delarue
R355 Discovery Miles 3 550 Ships in 10 - 15 working days
Le Guide de la Sante, Ou Tableaux Complets Des Maladies Secretes. 3e Edition (French, Paperback): Francois Delarue Le Guide de la Sante, Ou Tableaux Complets Des Maladies Secretes. 3e Edition (French, Paperback)
Francois Delarue
R459 Discovery Miles 4 590 Ships in 10 - 15 working days
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