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The first-passage density of a continuous gaussian process to a general boundary

Published online by Cambridge University Press:  14 July 2016

J. Durbin
J. Durbin*
Affiliation:
London School of Economics and Political Science
*
∗Postal address: The London School of Economics and Political Science, Department of Statistical and Mathematical Sciences, Houghton St, London WC2A 2AE, UK.
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Abstract

Under mild conditions an explicit expression is obtained for the first-passage density of sample paths of a continuous Gaussian process to a general boundary. Since this expression will usually be hard to compute, an approximation is given which is computationally simple and which is exact in the limit as the boundary becomes increasingly remote. The integral of this approximating density is itself approximated by a simple formula and this also is exact in the limit. A new integral equation is derived for the first-passage density of a continuous Gaussian Markov process. This is used to obtain further approximations.

Keywords

BROWNIAN MOTIONCONTINUOUS MARKOV PROCESSBOUNDARY-CROSSING PROBABILITYEXIT DENSITYVOLTERRA INTEGRAL EQUATION OF THE SECOND KIND
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 99 - 122
Copyright
Copyright © Applied Probability Trust 1985 

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