Methodology and Computing in Applied Probability

, Volume 10, Issue 4, pp 621–644 | Cite as

First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes



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.


Diffusion processes Boundary crossing First passage time density 

AMS 2000 Subject Classification

Primary 60J60 Secondary 60J70 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia

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