## Expectation functionals associated with some stochastic evolution equations.(English)Zbl 0618.60076

Stochastic partial differential equations and applications, Proc. Conf., Trento/Italy 1985, Lect. Notes Math. 1236, 40-56 (1987).
[For the entire collection see Zbl 0602.00007.]
The transition probabilities of a usual diffusion process (i.e., a process obeying the Ito-equation) satisfy a standard pde known as diffusion equation. The infinitely dimensional Ito-equation is considered. The main goal of the paper is to give an appropriate meaning of the corresponding infinitely dimensional analogue of the diffusion equation. Such an analogue naturally involves variational derivatives. A special case of a nonlinear Ito-equation in infinite dimensions is also discussed. Only the outlines of some proofs are given.
Reviewer: O.Enchev

### MSC:

 60J60 Diffusion processes 58J65 Diffusion processes and stochastic analysis on manifolds

Zbl 0602.00007