Applications of random process excursion analysis. Translated from the Russian by Dmitri Arch (Q2841393)

The monograph contains seven chapters and four appendixes, with one external.NEWLINENEWLINEThe first chapter of the book describes typical methods applied for studying parameters of excursion in broadband random processes, furthermore a few examples of using excursion statistics in practice can be found there.NEWLINENEWLINENew results and engineering applications of the considered theory are presented in Chapters 2--6.NEWLINENEWLINENEWLINEChapter 2 is divided into three sections. The author starts with providing both estimation and accurate calculation of informative parameters for excursion in Gaussian stationary random processes. Next, she obtains upper and lower estimates for distribution functions of time intervals between an arbitrarily chosen moment and the first zero crossing of the random process or the first moment when zero level is crossed in a given direction.NEWLINENEWLINENEWLINEChapter 3 contains three sections. At the beginning, estimations similar to those considered in the two last sections of the second chapter are obtained. Furthermore, the author shows that the distribution law for momentary values of centered non-Gaussian processes does have a significant effect on the characteristics of excursion, which are mainly determined by the waveform and root-mean-square frequency of the process power spectrum.NEWLINENEWLINENEWLINEIn Chapter 4, she concentrates on estimating parameters for exponential tails of distribution curves representing the distribution of such excursion that are much longer than the process time correlation interval.NEWLINENEWLINENEWLINEChapter 5 contains three sections. In the first one, the author explains how to use the generation sequence obtained by bilateral clipping on level zero of a centered random process. The additional information is carried by the sequence obtained in this way. This information is useful in reducing the error of calculating the parameters of zero crossing, by increasing the number of sequences. The second section explains how to extend the method based on the use of a generating pulse sequence to random processes of arbitrary kind including the noncentered and non-Gaussian ones. The third section is devoted to show how the distribution function of the total duration of \(i\) successive intervals is calculated.NEWLINENEWLINEChapter 6 contains two sections and concentrates on two characteristics of random process excursion. In the first section, the author shows a method allowing to estimate, on the basis of the results obtained in Chapter~5, the cumulative function and distribution density of time intervals between an arbitrarily chosen moment and the next moment when the stationary differentiable random process reaches the set level. The second section describes a method of estimating exponential tail parameters for distribution of areas enveloped by relatively long excursions.NEWLINENEWLINENEWLINEIn Chapter 7, she shows some algorithms for building digital adaptive analysers of stationary random process characteristics, furthermore some estimates of statistical errors and measurement times can be found there.NEWLINENEWLINENEWLINETo the best of the reviewer's knowledge, the present book is unique in its description of some of the aspects of the theory of excursions for random processes and its applications. It contains very interesting ideas and applications and should be equally useful for senior university students as well as for scientists and engineers.