First passage of nonstationary random processes

It is shown that a two- state Markov process for barrier passage statistics provides a more realistic model than the Poisson process, especially for the response of a lightly- damped oscillator to broad- bank excitation. For high barrier levels the two give similar results. With the Markov model, first passage probability depends on the first three area moments of the process power spectral density. The concept of a time- dependent power spectrum presented describes the frequency decomposition of the response of an oscillator suddenly exposed to broadband stationary excitation.