State-Estimation of Partially-Observed Markov Chains: Decomposition, Convergence, and Component Identification

Abstract

A partially-observed Markov chain (s,Y) consists of an N-state Markov chain S, along with a process Y of noisy observations of the transitions of S. A metric on stochastic N-vectors and a generalized ergodic coefficient on the transition probability matrices of (S,Y) are defined, resulting in a notion (similar to weak ergodicity) of deteriorating dependence on initial value in a process of distributions of the state (of S) conditioned on past observations. If (S, Y) is stationary, then S may be decomposed into M < or = N components, where M=1 neither implies nor is implied by ergodicity of S, such that conditional state distributions within each component geometrically approach an initial-value-independent process in the manner described above, and one or more equivalent components eventually dominate the others. A method for drift-free finite-memory approximation (or realization) of this process is also introduced.

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Document Details

Document Type
Technical Report
Publication Date
Dec 15, 1977
Accession Number
ADA050344

Entities

People

  • Loren K. Platzman

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Automata
  • Classification
  • Coefficients
  • Convergence
  • Decomposition
  • Ergodic Processes
  • Identification
  • Markov Chains
  • Markov Processes
  • Observation
  • Probability
  • Probability Distributions
  • Random Variables
  • Scientific Research
  • Stationary
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.