Extremes and Related Properties of Random Sequences and Processes

by M. R. Leadbetter, G. Lindgren, H. Rootzen

Overview

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.

Product Details

ISBN-13:	9781461254515
Publisher:	Springer New York
Publication date:	11/10/2011
Series:	Springer Series in Statistics
Edition description:	Softcover reprint of the original 1st ed. 1983
Pages:	336
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

I Classical Theory of Extremes.- 1 Asymptotic Distributions of Extremes.- 2 Exceedances of Levels and kth Largest Maxima.- 2.1. Part II Extremal Properties of Dependent Sequences.- 3 Maxima of Stationary Sequences.- 4 Normal Sequences.- 5 Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima.- 6 Nonstationary, and Strongly Dependent Normal Sequences.- 6.1. Part III Extreme Values in Continuous Time.- 7 Basic Properties of Extremes and Level Crossings.- 8 Maxima of Mean Square Differentiable Normal Processes.- 9 Point Processes of Upcrossings and Local Maxima.- 10 Sample Path Properties at Upcrossings.- 11 Maxima and Minima and Extremal Theory for Dependent Processes.- 12 Maxima and Crossings of Nondifferentiable Normal Processes.- 13 Extremes of Continuous Parameter Stationary Processes.- Applications of Extreme Value Theory.- 14 Extreme Value Theory and Strength of Materials.- 15 Application of Extremes and Crossings Under Dependence.- Appendix Some Basic Concepts of Point Process Theory.- List of Special Symbols.