Exponential power series expansion for the propagator of general diffusion processes

Abstract

The propagator of a general diffusion process is determined by expanding its exponent in a power series of a time increment t. The expansion coefficients can be analytically evaluated from recursive relations. We are thus able to construct a covariant short time approximation for the propagator valid to any desired precision in t. Attention is given both to the mathematics and its physical interpretation. This allows us to shed further light on the results already known in the literature on quantum mechanics and theory of continuous Markov processes.