First passage densities and boundary crossing probabilities for diffusion processes
Andrew N Downes, Konstantin Borovkov
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | SPRINGER | Published : 2008
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 this is extended to a lower bound, as well as bounds for the first crossing time of a lower boundary. An extension to some time-inhomogeneous diffusions is given. These results are illustrated by numerical examples. © Springer Science+Business Media, LLC..View full abstract
This research was supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems. The authors are grateful for the comments made by the referee, which helped to improve the paper.