AN APPROACH TO SEMI-MARKOV PROCESSES

Abstract

The paper reports on some of the mathematical results that the author obtained while seeking to refine Markov chain models. In an effort to take into account the waiting time in each state prior to transition, a non-Markov process was postulated. Subsequent investigation showed the process to be a reformulation of a semi-Markov process. In the present case, the equations for the flow resemble a multi-dimensional renewal process. The behavior of the system is described by a probability density which characterizes the process at any time t > 0, given that the states of the process were defined at time t = 0. It is shown in the special steady state case that the probability distribution yields results which are equivalent to those previously given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 23, 1970
Accession Number
AD0703537

Entities

People

  • Stephen Saperstone

Organizations

  • Center for Naval Analyses

Tags

DTIC Thesaurus Topics

  • Clocks
  • Convolution Integrals
  • Differential Equations
  • Economic Development
  • Equations
  • Intervals
  • Kolmogorov Equations
  • Markov Chains
  • Markov Processes
  • Partial Differential Equations
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Real Numbers
  • Steady State
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.