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Approximation to the exit probability of a continuous Gaussian process over a U-shaped boundary of increasing curvature

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

A. N. Balabushkin
A. N. Balabushkin*
Affiliation:
Institute of Control Sciences, Moscow
*
∗Postal address: 1–267 Proizvodstvennaya Street, Moscow 119619, Russia.
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Abstract

A simple approximation to the probability of crossing a U-shaped boundary by a Brownian motion is given. The larger the second derivative of the curve at a minimum point, the higher the accuracy of the approximation. The result is also extended to a class of continuous Gaussian processes with definite properties. Numerical examples are given.

Keywords

BROWNIAN MOTIONCONTINUOUS GAUSSIAN PROCESSBOUNDARY CROSSING

MSC classification

Primary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 429 - 442
Copyright
Copyright © Applied Probability Trust 1995 

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References

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