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The two-barrier problem for continuously differentiable processes

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Igor Rychlik
Igor Rychlik*
Affiliation:
University of Lund
*
∗ Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221–00 Lund, Sweden.
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Abstract

An efficient algorithm to compute upper and lower bounds for the first-passage time in the presence of a second absorbing barrier by means of a continuously differentiable decomposable process, e.g. a smooth function of a continuously differentiable Gaussian vector field, is given. The method is used to obtain accurate approximations for the joint density of the zero-crossing wavelength and amplitude and the distribution of the rainflow cycle amplitude. Numerical examples illustrating the results are also given.

Keywords

CROSSINGSFATIGUEFIRST-PASSAGE DENSITYRAINFLOW CYCLEWAVEHEIGHTWAVELENGTH

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60G17: Sample path properties

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 71 - 94
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by the Swedish Natural Science Research Council, Grant No F-PD 9280–100, and by the Air Force Office of Scientific Research, Grant No. F49620 85C 0144 at the University of North Carolina, Chapel Hill.

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