This talk will address a new link between stochastic dierential equations (SDEs) and nonlinear parabolic PDEs. Starting from the condition of path-independence of Girsanov transform density for the stochastic dierential
> > equations, I will establish the derivation of the new link. Extensions to the case of SDEs on dierential manifolds as well as to that of (in nite dimensional) SDEs on separable Hilbert spaces will be discussed. An application to a stochastically deformed dynamical system will be briey considered.