# First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

#### by Andrew Downes

Institution: MASCOS, The University of Melbourne
Date: Fri 18th April 2008
Time: 3:15 PM
Location: Theatre 1, Grd floor ICT Building, 111 Barry St, Uni of Melb

Abstract: We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one.
In doing so we establish the existence of the first-passage time density and provide an upper bound for this function. In the case of
processes with diffusion interval equal to $\mathbb{R}$ this is extended to a lower bound, as well as bounds for the first crossing
time of a lower boundary. These results are illustrated by numerical
examples.

*** Drinks and nibbles will be served at MASCOS, 139 Barry St, after the
seminar