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.
KeywordsDiffusion processes Boundary crossing First passage time density
AMS 2000 Subject ClassificationPrimary 60J60 Secondary 60J70
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