Extremal and Related Properties of Stationary Processes. Part II. Extreme Values in Continuous Time.

Abstract

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 < or = t < or = T), where Xi(t) is a stationary stochastic process satisfying appropriate regularity and dependence conditions. Cases where the process (Xi(t)) is normal are discussed in detail. Related topics include point process properties of upcrossings of levels, sample path properties at such upcrossings, location of extremes, maxima and minima for two or more dependent processes, and properties of local extremes. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1980
Accession Number
ADA092163

Entities

People

  • G. Lindgren
  • H. Rootzen
  • M. Ross Leadbetter

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Analogs
  • Convergence
  • Covariance
  • Data Science
  • Distribution Functions
  • Ergodic Processes
  • Gaussian Processes
  • Information Science
  • Intensity
  • Markov Processes
  • Mathematical Analysis
  • New York
  • Probability
  • Random Variables
  • Stationary Processes
  • Stochastic Processes
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.