Abstract
We derive the dynamical equations for stochastic processes and for quantum mechanics from a variational principle in terms of the stochastic action. We introduce canonical transformations for stochastic Markoffian functions and we derive a stochastic Hamilton-Jacobi equation. By means of a change of function we linearize the latter and obtain an equation for the probability amplitude (Sohrödinger’s equation for the quantal case). We discuss Feynman’s path integral method in this context, using the stochastic action. Both diffusion processes and quantum mechanics are discussed simultaneously by means of a quantity ɛ whose square is 1 for the first case and —1 for the latter.
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