On the asymptotic behavior of first passage time densities for stationary Gaussian processes

Details On the asymptotic behavior of first passage time densities for stationary Gaussian processes On the asymptotic behavior of first passage time densities for stationary Gaussian processes

2003-05-16

arxiv.org/abs/math/0305240v2

Mathematics

Probability

21 pages, 7 figures, to be published in Methodology and Computing in Applied Probability

Scientific paper

Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries, is determined. Sufficient conditions are then given such that the density asymptotically exhibits an exponential behavior when the boundary is either asymptotically constant or asymptotically periodic.

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