Independent Sampling of a Stochastic Process

Abstract

We investigate when sampling a stochastic process X = (X(t) : t > 0) at the times of an independent point process, leads to the same empirical distribution as the time average limiting distribution of X. Two cases we considered. The first is when X is an asymptotically stationary process and satisfies a mixing and coupling condition. In this case, the entire limiting distribution in function space are shown to be the same. The second case is when X is only assumed to have a constant finite time average and is assumed a positive t renewal with a spread-out cycle length distribution. In this non-ergodic case, the averages are shown to be the when some condition we placed on X.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1991
Accession Number
ADA249712

Entities

People

  • Karl Sigman
  • Peter W. Glynn

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Couplings
  • Engineering
  • Ergodic Processes
  • Industrial Engineering
  • Markov Chains
  • Markov Processes
  • Military Research
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Sampling
  • Stationary
  • Stationary Processes
  • Stochastic Processes
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.

Technology Areas

  • Space