ABSTRACT
The sojourn time distribution of a diffusion process is, as is well known, uniquely identified as the solution of a differential equation associated with the generator of the process. This chapter discusses that a direct probabilistic approach yields explicit asymptotic estimates of the sojourn distribution without having to find explicit solutions of the differential equations. It reviews relevant facts from diffusion theory. By a direct extension of V. A. Volkonskii’s arguments, any diffusion can also be transformed into a Brownian motion with negative linear drift. The “scale function” of the diffusion has a central role in the transformation. Local time for diffusion is conventionally defined as the derivative of the sojourn time distribution with respect to the speed measure.
