# Accession Number:

## ADA050344

# Title:

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

# Descriptive Note:

## Interim rept.

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB

# Personal Author(s):

# Report Date:

## 1977-12-15

# Pagination or Media Count:

## 45.0

# 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 M1 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability