The first passage time problem through a monotone boundary is considered for stationary Gaussian processes possessing rational spectral densities. Using a parallel procedure to simulate sample paths, estimates of the upcrossing probability density function of the first passage time are constructed. A comparison is provided with the numerical results obtained by Kostyukov via numerical solution of a Volterra integral equation. Finally, the effect of covariance's oscillatory components and of the behaviour of the boundary on the shape of the upcrossing FPT densities are pinpointed.

Estimating upcrossing FPT densities via simulation of Gaussian processes

PIROZZI, ENRICA;RICCIARDI, LUIGI MARIA
1997

Abstract

The first passage time problem through a monotone boundary is considered for stationary Gaussian processes possessing rational spectral densities. Using a parallel procedure to simulate sample paths, estimates of the upcrossing probability density function of the first passage time are constructed. A comparison is provided with the numerical results obtained by Kostyukov via numerical solution of a Volterra integral equation. Finally, the effect of covariance's oscillatory components and of the behaviour of the boundary on the shape of the upcrossing FPT densities are pinpointed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/174833
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