More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package

摘要

Version 1.2 of the fptdApprox R package implemented a general heuristic strategy for the efficient application of numerical schemes aimed at solving Volterra integral equations whose solutions are first-passage-time (f.p.t.) density functions for a diffusion process.This paper presents a new version of this package, developed with the goal of addressing interesting f.p.t. problems that cannot be solved with the previous version. More specifically, it addresses f.p.t. problems for diffusion processes defined by means of not-closed-form time expressions (which appear in application fields such as tumor growth or the evolution of economic variables), and unconditioned f.p.t. problems for diffusion processes with non-degenerate initial distributions (of great interest in the study of population growth in Biology and Ecology).Here, the functionality of this new version is described, with a focus on its numerical and computational aspects.Moreover, by means of several examples, we show how the package can be used to solve problems such as those mentioned above.