Weakly dependent stochastic sequences and their applications. Vol. XII: Random sums, extremes and sequential analysis (Q2763509)

This is the final volume in Yoshihara's monumental 12-volume encyclopaedia on weakly dependent processes. To give an idea of the contents, we list the titles of the chapters: 1. Foundations, 2. Random sums, 3. Large deviation principles, 4. Excursion random measures, 5. Exceedance and first passage times, 6. Extremal properties of some statistics, 7. GARCH processes, 8. Sequential analysis, 9. Change-point problems.NEWLINENEWLINENEWLINEChapter 2 is devoted to weak convergence of random sums of triangular arrays. The main part concerns rowwise independent arrays, followed by a short section on random sums of strong mixing sequences. Chapter 3 presents large deviation principles for empirical measures of strongly mixing processes, and for empirical \(U\)-processes of dependent observations. Chapters 4 to 7 are devoted to the study of extremal behavior of various types of stationary processes. Chapter 4 introduces point processes of exceedances and the convergence of partial sums via point process techniques, including applications of these techniques to stable convergence of partial sums and convergence of tail array sums of strongly mixing processes. Chapter 5 studies large deviations of exceedances and first passage times for vector-valued processes. In Chapter 6, among other things, the extremal index of stationary sequences and related statistics, such as the tail empirical and quantile processes and the Hill estimator are investigated. Chapter 7 introduces GARCH processes, and studies their extremes and sample autocorrelations. Chapter 9 is devoted to sequential analysis of dependent processes, with least-squares estimation in a threshold AR(1)-model and fixed width sequential confidence regions as special topics. In the final section the detection of change points in multivariate dependent processes is investigated.NEWLINENEWLINENEWLINEAs in the first 11 volumes of this series, a large number of topics is covered in this final volume, making this a useful reference for researchers. A drawback is the fact that the presentation is usually very close to specific original papers.