LIMITING COVARIANCE IN MARKOV-RENEWAL PROCESSES

Abstract

General additive functions called rewards are defined on a 'regular' finite-state Markov-renewal process. The asymptotic form of the mean total reward in (O, t) has previously been obtained, and it is known that the total rewards are joint-normally distributed as t approaches infinity. This paper finds the dominant asymptotic term in the covariance of the total rewards as a simple function of the moments of the per-transition rewards, and the 'bias' term of the mean total rewards. Special formulas for the dominant covariance term of 'number of visits', and 'occupation time' in given states are also derived.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 22, 1964
Accession Number
AD0605500

Entities

People

  • William S. Jewell

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Business Administration
  • Covariance
  • Dynamic Programming
  • Equations
  • Maintenance
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Navy
  • New Jersey
  • New York
  • Operations Research
  • Probability
  • Random Variables
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.