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On the two sided barrier problem

Published online by Cambridge University Press:  14 July 2016

Masanobu Shinozuka
Masanobu Shinozuka*
Affiliation:
Columbia University, New York
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Abstract

Upper and lower bounds are given for the probability that a separable random process X(t) will take values outside the interval (— λ 1, λ 2) for 0 ≦ t ≦ T, where λ 1 and λ 2 are positive constants.

The random process needs to be neither stationary, Gaussian nor purely random (white noise).

In engineering applications, X(t) is usually a random process decaying with time at least in the long run such as the structural response to the acceleration of ground motion due to earthquake.

Numerical examples show that the present method estimates the probability between the upper and lower bounds which are sufficiently close to be useful when the random processes decay with time.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 79 - 87
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Rice, S. O. (1954) Mathematical analysis of random noise. Selected Papers on Noise and Stochastic Processes. Editor Wax, N. Dover, New York. 190.Google Scholar
[2] Moyal, J. E. (1949) Statistical processes and statistical physics. J. R. Statist. Soc. B, 11, 168–180.Google Scholar
[3] Ibid. 167.Google Scholar
[4] Bendat, J. S. (1958) Principles and Applications of Random Noise Theory. John Wiley, New York. 127.Google Scholar
[5] Jahnke, E. and Emde, F. (1945) Tables of Functions. Dover, New York. 6–7.Google Scholar
[6] Birnbaum, Z. W. and Marshall, A. W. (1961) Some multivariate Chebyshev inequalities with extensions to continuous parameter process. Ann. Math. Statist. 32, 687–703.CrossRefGoogle Scholar
[7] Slepian, D. (1962) The one sided barrier problem for Gaussian noise. Bell System Technical Journal 41, 463–501.Google Scholar
[8] Newell, G. F. and Rosenblatt, M. (1962) Zero crossing probabilities for Gaussian stationary processes. Ann. Math. Statist. 33, 1306–1313.Google Scholar
[9] Cramér, H. (1962) On the maximum of a normal stationary stochastic process. Bull. Amer. Math. Soc. 68, 515.Google Scholar