Probability Characteristics of Random Processes
Statistics of above-threshold excursions of a random process are useful in solving many problems of practical importance. 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 in such a way that 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, the distribution of extrema amplitudes, etc. A random process structure can be described only if we know all of the above random variables. They provide more information on the process than integral characteristics, such as the power spectrum and correlation function.

Section 1.1 offers a short historical sketch of methods applied for studying parameters of excursions in broadband random processes. Some examples of using excursion statistics for practical purposes are given in Section 1.2.

The areas of application covered include telecommunications, radio positioning, medical instrumentation industry, estimating excessive load in mechanical structures, estimating the impact of ionospheric and tropospheric factors on radio wave propagation, and surface-finish monitoring, to mention just a few.