First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes |
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Authors: | Andrew N Downes Konstantin Borovkov |
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Institution: | (1) Department of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria, Australia, 3010 |
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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.
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Keywords: | Diffusion processes Boundary crossing First passage time density |
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