Oskar Hagberg

Approximating the rate of crossings of a function of a vector valued
Gaussian process

Abstract:

A class of one-dimensional stationary non-Gaussian processes is the
class of random processes which can be expressed as a sufficiently
smooth real valued function of a vector valued differentiable,
stationary Gaussian process. The crossing intensity  of a fixed level
is a function of the joint correlation structure of the process and
its derivative, but in general no simple exact form is known. However,
in 1988 Karl Breitung gave an asymptotic expression valid as the level
tends to infinity and when the function is subject to certain
conditions, but he didn't attempt to estimate the error. We will study
how the conditions could be relaxed and how the error can be estimated
as a second term in an asymptotic expansion.