External Theory for Stochastic Processes.

Abstract

The purpose of this paper is to provide an overview of the asymptotic distributional theory of extreme values for a wide class of dependent stochastic sequences and continuous parameter processes. The theory contains the standard classical extreme value results for maxima and extreme order statistics as special cases but is richer on account of the diverse behavior possible under dependence in both discrete and continuous time contexts. Emphasis is placed on stationary cases but other important classes (e.g. Mark of sequences) are included. Significant ideas and methods are described rather than details, and in particular the nature and role of important underlying point processes (such as exceedances and upcrossings) are emphasized. Applications are given to particular classes of process (e.g. normal, moving average) and connections with related theory (such as convergence of sums) are indicated.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1985
Accession Number
ADA179145

Entities

People

  • Holger Rootzen
  • M. R. Ledbetter

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Convergence
  • Data Science
  • Differential Equations
  • Equations
  • Gaussian Processes
  • Information Science
  • Markov Chains
  • Mathematics
  • Normal Distribution
  • Order Statistics
  • Probability
  • Random Variables
  • Stationary Processes
  • Statistics
  • Stochastic Processes
  • Surveys
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.