The notion of a non-stationary narrow-band stochastic process is introduced without reference to a frequency spectrum, and the joint distribution function of two consecutive maxima is approximated by use of an envelope. Based on these definitions the first passage problem is treated as a Markov point process. The theory is applied to the response of a linear oscillator excited by a stationary process from t = 0, and a simple algebraic relation between the non-stationary and stationary correlation functions of the response is derived.

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