On the First-Passage Distribution for the Envelope of a Nonstationary Narrow-Band Stochastic Process

[+] Author and Article Information
W. C. Lennox, D. A. Fraser

Department of Civil Engineering, University of Waterloo, Waterloo, Ontario, Canada

J. Appl. Mech 41(3), 793-797 (Sep 01, 1974) (5 pages) doi:10.1115/1.3423390 History: Received August 01, 1973; Revised January 01, 1974; Online July 12, 2010


A narrow-band stochastic process is obtained by exciting a lightly damped linear oscillator by wide-band stationary noise. The equation describing the envelope of the process is replaced, in an asymptotic sense, by a one-dimensional Markov process and the modified Kolmogorov (backward) equation describing the first-passage distribution function is solved exactly using classical methods by reducing the problem to that of finding the related eigenvalues and eigenfunctions; in this case degenerate hypergeometric functions. If the exciting process is white noise, the analysis is exact. The method also yields reasonable approximations for the first-passage time of the actual narrow-band process for either a one-sided or a symmetric two-sided barrier.

Copyright © 1974 by ASME
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