State-Estimation of Partially-Observed Markov Chains: Decomposition, Convergence, and Component Identification
MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB
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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.
- Statistics and Probability