Last works. Publication edited by Laboratoires de Mathématiques Pures et Appliquées de l'Université Blaise Pascal, Clermont-Ferrand, France. (Q1354650)

This work was edited for a colloquium held in memory of Albert Badrikian, who died while mountaineering on 31st July, 1994. It contains four parts. The first part (11 pages), in French, analyses the mathematical work of A. Badrikian and gives a complete list of his publications. This work is an important monograph on random linear functions and cylindrical measures, probabilities on Banach spaces, anticipative stochastic calculus and Feynman's integral. The second part (46 pages), in English, was a lecture given in Santiago de Chile in 1991. It is devoted to the transformation of Gaussian measures and is motivated by the following problem: Let \((X,{\mathcal F},\mu)\) be a measured space and \(T:X\to X\) measurable, when the image \(T(\mu)\) of \(\mu\) by \(T\) is absolutely continuous with regards to \(\mu\), and how do we calculate the density? The first chapter is devoted to anticipative stochastic integrals and gives the main results. The second one studies the transformation of a Gaussian measure and the last one, the transformation by anticipative flows. The third part (55 pages), also in English, was given as several lectures at a Seminar in Clermont-Ferrand in 1993-94. The first chapter introduces the Wiener measure on Lusin spaces, the Cameron-Martin space and gives many examples (Brownian motion, Brownian bridge, Wiener product spaces, Brownian motion in an abstract Wiener space). The second one studies the application of measurable linear operators on a Wiener space, then compares them with Cameron-Martin spaces. An application is given for Brownian motions in infinite dimension. The fourth part (57 pages), in French, would have been the first chapters of a book on Hilbertian semi-martingales. The first chapter recollects the definitions and properties of Hilbertian spaces and nuclear applications. The second chapter introduces Hilbertian martingales and corresponding stochastic integrals. Written in the lively style of the author and printed in a pleasant way, this last work brings together, in didactic form, recent results which up until now were scattered.