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- W2009797918 abstract "Let ${X_n, n = 1, 2, cdots}$ be a Markov chain with finite state space $S = {1, 2, cdots, d}$, transition probability matrix $P$ and initial distribution $p$. Let $g$ be a function with $S$ as domain and define $Y_n = g(X_n)$. Define begin{align*}Z_n^i &= operatorname{Pr}lbrack X_n = i mid Y_1, Y_2, cdots, Y_n rbrack, Z_n &= (Z_n^1, Z_n^2, cdots, Z_n^d),end{align*} and let $mu_n$ denote the probability distribution of the vector $Z_n$. In this paper we prove that if ${X_n, n = 1, 2, cdots}$ is ergodic and if $P$ and $g$ satisfy a certain condition then $mu_n$ converges to a limit and this limit is independent of the initial distribution $p$." @default.
- W2009797918 created "2016-06-24" @default.
- W2009797918 creator A5063840868 @default.
- W2009797918 date "1975-08-01" @default.
- W2009797918 modified "2023-10-16" @default.
- W2009797918 title "A Limit Theorem for Partially Observed Markov Chains" @default.
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- W2009797918 doi "https://doi.org/10.1214/aop/1176996308" @default.
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