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