On the dynamics of diffusions and the related general electromagnetic potentials

In this paper the Nelson’s stochastic mechanics is extended to general diffusion motions. A representation theorem is proved which gives a one‐to‐one correspondence between solutions of certain Schrödinger equations and diffusion processes satisfying appropriate regularity conditions. Exploiting results of stochastic mechanics on Riemannian manifolds it is shown that the real part of the Schrödinger equations corresponding to the considered diffusions can be interpreted as Newton’s second law where the force is produced by generalized electromagnetic potentials.