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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 (— λ1, λ2) for 0 ≦ t ≦ T, where λ1 and λ2 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.

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

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