Stochastic differential geometry. (English. Russian original) Zbl 0541.60053
Russ. Math. Surv. 38, No. 3, 97-125 (1983); translation from Usp. Mat. Nauk 38, No. 3(231), 87-111 (1983).
The paper gives another exposition of what is now called ”Malliavin’s stochastic calculus”. The approach is somewhat close to the Bismut’s one. The results are extended to the case of diffusion processes on infinite dimensional smooth manifolds. This enables the author to construct certain quasi-invariant measures on infinite dimensional Lie groups such as groups of diffeomorphisms.
Reviewer: Y.Kifer
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
| 58D20 | Measures (Gaussian, cylindrical, etc.) on manifolds of maps |
| 28C10 | Set functions and measures on topological groups or semigroups, Haar measures, invariant measures |
