Some Peculiar Semi-Markov Processes

Abstract

Experience with semi-Markov processes with finite expected waits suggests that the behavior of Markov processes is a good guide to understanding the behavior of the more general process. However, examples are given to show that when expected waits are infinite quite surprising behavior is possible. For a two-state aperiodic semi-Markov process the instantaneous state probabilities Pi(t) can have (C, l)-limits but not strict limits; for a three-state (and irreducible) process one can have Po(t) tend to a strict limit as t - infinity but Pi(t) and P2(t)not even have (C, l)-limits. For an aperiodic irreducible infinite chain one can have Pi(t) - pi i > 0 as t - infinity, for every i, yet Epsilon pi i < 1.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD1027217

Entities

People

  • Walter L. Smith

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Distribution Functions
  • Markov Chains
  • Markov Processes
  • Military Research
  • North Carolina
  • Probability
  • Random Variables
  • Scientific Research
  • Time Intervals
  • Transitions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Mathematical Modeling and Probability Theory.