Applications of Random Process Excursion Analysis

Introduction

In spite of the fact that for decades excursions of stationary random processes have been the focus of attention of a number of researchers, the development of excursion theory is far from its completion. The reason for that is the difficulty of describing the subtle nature of random processes by means of mathematics, which would allow us to estimate a variety of distribution functions, for example, the distribution of widths of above-threshold excursions, the distribution of areas enveloped by the signal excursions, the distribution of time periods required for a signal to reach certain limits, and the distribution of extrema amplitudes.

Of all characteristics of random process excursions, the first approximations of excursion duration ...