Construction of first-passage-time densities for a diffusion process which is not necessarily time-homogeneous

Abstract

In Giorno et al. (1988) a new method for constructing first-passage-time probability density functions is outlined. This rests on the possibility of constructing the transition p.d.f. of a new time-homogeneous diffusion process in terms of a preassigned transition p.d.f. without making use of the classical space-time transformations of the Kolmogorov equation (Ricciardi (1976)).In the present paper we give an extension of this result to the case of a diffusion process X(t) which is not necessarily time-homogeneous, and a few examples are presented.