RATIO LIMIT THEOREMS FOR MARKOV CHAINS,

Abstract

In an irreducible, recurrent, Markov chain, with integer states, let N sub n(A) be the occupation time of A sy time n, where A is a finite set of states. The principal concern in this memorandum was to investigate various 'ratio limit theorems' for P sub x(N sub n(A) =k). Criteria were given for various ratio limits to exist. The limits (when they exist) were shown to be expressible in terms of an integral over the set of integers E completed with its dual recurrent boundary B. Applications were given to several specific Markov chains. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1964
Accession Number
AD0607976

Entities

People

  • Sidney C. Port

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Integrals
  • Markov Chains
  • Markov Processes
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research
  • Regression Analysis.