First and second-order approximations to the first passage time conditional probability density function of a stationary Gaussian process, with differentiable sample paths crossing a time-dependent boundary, are explicitly provided. In the limit of infinitely large time, our results coincide with the well-known results of Kac and Rice for the constant level-crossing problem.

A note on first passage time problems for Gaussian processes and varying boundaries

RICCIARDI, LUIGI MARIA;
1983

Abstract

First and second-order approximations to the first passage time conditional probability density function of a stationary Gaussian process, with differentiable sample paths crossing a time-dependent boundary, are explicitly provided. In the limit of infinitely large time, our results coincide with the well-known results of Kac and Rice for the constant level-crossing problem.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/159379
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