On Extremes of Stationary Processes
Title | On Extremes of Stationary Processes PDF eBook |
Author | M. R. Leadbetter |
Publisher | |
Pages | 23 |
Release | 1978 |
Genre | |
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).
Extremes and Related Properties of Random Sequences and Processes
Title | Extremes and Related Properties of Random Sequences and Processes PDF eBook |
Author | M. R. Leadbetter |
Publisher | Springer Science & Business Media |
Pages | 344 |
Release | 2012-12-06 |
Genre | 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.
Extremal and Related Properties of Stationary Processes. Part I. Extremes of Stationary Sequences
Title | Extremal and Related Properties of Stationary Processes. Part I. Extremes of Stationary Sequences PDF eBook |
Author | M. R. Leadbetter |
Publisher | |
Pages | 103 |
Release | 1979 |
Genre | |
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).
Stationary Stochastic Processes
Title | Stationary Stochastic Processes PDF eBook |
Author | Georg Lindgren |
Publisher | CRC Press |
Pages | 378 |
Release | 2012-10-01 |
Genre | 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.
On Extremes for Multidimensional Differentiable Stationary Processes
Title | On Extremes for Multidimensional Differentiable Stationary Processes PDF eBook |
Author | Patrick Albin |
Publisher | |
Pages | 60 |
Release | 1988 |
Genre | |
ISBN |
On Double Extremes of Gaussian Stationary Processes
Title | On Double Extremes of Gaussian Stationary Processes PDF eBook |
Author | A. Ladneva |
Publisher | |
Pages | 18 |
Release | 2000 |
Genre | |
ISBN |
Extremes of Stationary Processes
Title | Extremes of Stationary Processes PDF eBook |
Author | Richard Alan Davis |
Publisher | |
Pages | 244 |
Release | 1979 |
Genre | Stationary processes |
ISBN |