Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

الملخص EN

The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces.

Connection between solutions to the abstract stochastic differential equation dX(t)=AX(t)dt + BdW(t) and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic ?t,xh(X(T)) is proved.

Interpretation of objects in the equations is given.