First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

Andrew N. Downes () and Konstantin Borovkov ()
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Andrew N. Downes: University of Melbourne
Konstantin Borovkov: University of Melbourne

Methodology and Computing in Applied Probability, 2008, vol. 10, issue 4, 621-644

Abstract: 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 ℝ 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.

Keywords: Diffusion processes; Boundary crossing; First passage time density; Primary 60J60; Secondary 60J70 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-008-9070-x

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