Author : M. R. Leadbetter
Publisher :
Page : 103 pages
File Size : 28,8 MB
Release : 1979
Category :
ISBN :
This report considers the generalization of classical extreme value theory for independent random variables, to apply to stationary stochastic processes. Part 1 is concerned with stochastic sequences and part 2 will deal with continuous time processs. (Author).
Author : M. R. Leadbetter
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 10,5 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461254493
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Author : M. R. Leadbetter
Publisher :
Page : 151 pages
File Size : 33,38 MB
Release : 1980
Category :
ISBN :
In this work we explore extremal and related theory for continuous parameter stationary processes. A general theory extending that for the sequence case, described in Chapter 2 of Part I, is obtained, based on dependence conditions closely related to those used there for sequences. In particular, a general form of Gnedenko's Theorem is proved for the maximum M(T) = sup (Xi(t); 0
Author : M. R. Leadbetter
Publisher :
Page : 190 pages
File Size : 37,45 MB
Release : 1979
Category :
ISBN :
Author : M. R. Leadbetter
Publisher :
Page : 143 pages
File Size : 13,71 MB
Release : 1979
Category :
ISBN :
Author : M. R. Leadbetter
Publisher :
Page : 23 pages
File Size : 15,52 MB
Release : 1978
Category :
ISBN :
Certain aspects of extremal theory for stationary sequences and continuous parameter stationary processes, are discussed in this paper. A slightly modified form of a previously used dependence condition, leads to simple proofs of some key results in extremal theory of stationary sequences. Dependence conditions of a 'weak mixing' type are introduced for continuous parameter stationary processes and results of classical extreme value theory extended to that context. (Author).
Author : J. Tiago de Oliveira
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 32,85 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401730695
The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.
Author : Georg Lindgren
Publisher : CRC Press
Page : 378 pages
File Size : 11,62 MB
Release : 2012-10-01
Category : Mathematics
ISBN : 1466557796
Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Author : Pavle Mladenović
Publisher : Springer
Page : 0 pages
File Size : 47,62 MB
Release : 2024-06-04
Category : Mathematics
ISBN : 9783031574115
The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry. The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.
Author :
Publisher :
Page : 368 pages
File Size : 43,2 MB
Release : 1979
Category : Science
ISBN :
