Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries

Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparison of different diffusion models where first passage times represent an important feature and the determination of upper and lower bounds for first passage time distributions.