On the two sided barrier problem

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Abstract
Upper and lower bounds are given for the probability that a separable random processX(t) will take values outside the interval (—λ1,λ2) for 0 ≦t≦T, whereλ1andλ2are 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.

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