Analyse différentielle sur l’espace de Wiener. (French) Zbl 0567.60045
Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 1089-1096 (1984).
[For the entire collection see Zbl 0553.00001.]
The paper presents theses of a report on the stochastic analysis of variations. The notion of a derivative on a Wiener space is discussed. The following questions are treated: the connection between this derivative and Ornstein-Uhlenbeck processes, the stochastic calculus based on these notions, the problems of differential geometry on a Wiener space, implicit function theorems in terms of capacity, the stationary phase method, etc. Applications of this calculus to problems of regularity of measures in elliptic and hypoelliptic cases, in an infinite dimension case and in a filtering problem, are briefly outlined.
The paper presents theses of a report on the stochastic analysis of variations. The notion of a derivative on a Wiener space is discussed. The following questions are treated: the connection between this derivative and Ornstein-Uhlenbeck processes, the stochastic calculus based on these notions, the problems of differential geometry on a Wiener space, implicit function theorems in terms of capacity, the stationary phase method, etc. Applications of this calculus to problems of regularity of measures in elliptic and hypoelliptic cases, in an infinite dimension case and in a filtering problem, are briefly outlined.
Reviewer: A.Yu.Veretennikov
MSC:
| 60G30 | Continuity and singularity of induced measures |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
