Ecole d'Ete de Probabilites de Saint-Flour XXI - 1991


Book Description

CONTENTS: D.D. Dawson: Measure-valued Markov Processes.- B. Maisonneuve: Processus de Markov: Naissance, Retournement, Regeneration.- J. Spencer: Nine lectures on Random Graphs.




Ecole d'Ete de Probabilites de Saint-Flour XX - 1990


Book Description

CONTENTS: M.I. Freidlin: Semi-linear PDE's and limit theorems for large deviations.- J.F. Le Gall: Some properties of planar Brownian motion.







Monte Carlo and Quasi-Monte Carlo Methods 2004


Book Description

This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas.




Mean Field Games


Book Description

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.




Optimal Transport


Book Description

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.




Ecole d'Ete de Probabilites de Saint-Flour XVIII - 1988


Book Description

This book contains three lectures each of 10 sessions; the first on Potential Theory on graphs and manifolds, the second on annealing and another algorithms for image reconstruction, the third on Malliavin Calculus.




Ecole d'Ete de Probabilites de Saint-Flour XX - 1990


Book Description

CONTENTS: M.I. Freidlin: Semi-linear PDE's and limit theorems for large deviations.- J.F. Le Gall: Some properties of planar Brownian motion.