Background
Bouleau, Nicolas André was born on May 20, 1945 in Paris. Son of Charles and Wanda (Rabaud) Bouleau.
(The subject of this book is analysis on Wiener space by m...)
The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss carre du champ operators introduced by Meyer and Bakry very carefully. Although they discuss when this carre du champ operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of carre du champ operator in this case by using Shigekawa s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Ito-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo) "
http://www.amazon.com/gp/product/3110129191/?tag=2022091-20
(Gives greater rigor to numerical treatments of stochastic...)
Gives greater rigor to numerical treatments of stochastic models. Contains Monte Carlo and quasi-Monte Carlo techniques, simulation of major stochastic procedures, deterministic methods adapted to Markovian problems and special problems related to stochastic integral and differential equations. Simulation methods are given throughout the text as well as numerous exercises.
http://www.amazon.com/gp/product/0471546410/?tag=2022091-20
Bouleau, Nicolas André was born on May 20, 1945 in Paris. Son of Charles and Wanda (Rabaud) Bouleau.
Diploma in engineering, Ecole Polytechnic, Paris, 1967. Degree in engineering, Ecole Ponts et Chaussees, Paris, 1970. Government diploma in architecture, Ecole des Beaux Arts, Paris, 1972.
Thèse d'Etat, University Paris VI, 1980. Habilitation, University Paris VI, 1987.
Civil engineer Public Urban Planning, Torcy, France, 1970-1975. Researcher Ecole Polytechnique, Palaiseau, France, 1975-1981. Researcher, professor Ecole des Ponts, Paris, since 1981.
Director Research Center Applied Mathematics, Noisy, 1984-1993. Member science council National Geography Institute, 1986.
(The subject of this book is analysis on Wiener space by m...)
(Gives greater rigor to numerical treatments of stochastic...)
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Author: Probabilites de l'Ingenieur, 1986, Processus Stochastiques et Applications, 1988, Martingales et marchés Financiers, 1998, Philosophies des Mathématiques et de la Modélisation, 1999. Co-author: Dirichlet Forms and Analysis on Wiener Space, 1991, Numerical Methods for Stochastic Processes, 1994. Editor in chief Annales des Ponts, since 1993.
Administration board Ecole National des Ponts et Chaussees, Paris., 1994. 2nd lieutenant French Infantry, 1967-1968. Member Laplace-Gauss Association (treasurer since 1992), Civil Engineering Research Committee, Mathematics Society France (secretary 1985-1989).
Married Sylvie Berline, May 31, 1968 (div. 1993); 4 children.