A NOTE ON THE VOLTERRA INTEGRAL-EQUATION FOR THE FIRST-PASSAGE-TIME PROBABILITY DENSITY

In this paper we prove the validity of the Volterra integral equation for the evaluation of first-passage-time probability densities through varying boundaries, given by Buonocore et al. [1], for the case of di ffusion processes not necessarily time-homogeneous. We study, specific ally those processes that can be obtained from the Wiener process in t he sense of [5]. A study of the kernel of the integral equation, in th e same way as that by Buonocore et al. [1], is done. We obtain the bou ndaries for which closed-form solutions of the integral equation, with out having to solve the equation, can be obtained. Finally, a few exam ples are given to indicate the actual use of our method.