THE LEARNING BEHAVIOR AND ERGODIC PROPERTY OF FINITE-STATE MARKOV CHAINS.

Abstract

The dynamic behavior of ergodic finite-state homogeneous Markov chains is studied. An ergodicity test of general natural is formulated. From this general test procedure, various test criteria are derived. One criterion is shown to be both necessary and sufficient. The ergodicity is found to be a topological property of the state flow graph of a finite-state homogeneous Markov chain or an equivalent stochastic automation. The dynamic behavior of an ergodic chain can be explained as a contraction mapping in the probability vector space. The norm of the induced transition probability matrix serves as pessimistic estimation of the learning rate.

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0653116

Entities

People

  • H. H. Yeh
  • J. T. Tou

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Automation
  • Ergodic Processes
  • Learning
  • Markov Chains
  • Markov Processes
  • Mathematics
  • Probability
  • Random Variables
  • Stochastic Processes
  • Transitions
  • Vector Spaces

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.

Technology Areas

  • Space