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First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

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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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Correspondence to Andrew N. Downes.

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Downes, A.N., Borovkov, K. First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes. Methodol Comput Appl Probab 10, 621–644 (2008). https://doi.org/10.1007/s11009-008-9070-x

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  • DOI: https://doi.org/10.1007/s11009-008-9070-x

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