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Limit theorems for conditional Markov chains

Z. I. Bežaeva

Moscow

Abstract: Let $\zeta_k(\omega)=(\xi_k(\omega),\eta_k(\omega))$ ($k=1,2,\dots$) be a finite homogeneous Markov chain. If $\eta_1(\omega),\dots,\eta_n(\omega)$ are fixed, $\xi_k$ ($k=1,\dots,n$) are known to be a so-called conditional Markov chain.
In this paper, the law of large numbers and the central limit theorem for the conditional Markov chain are obtained.

Received: 20.03.1970

 English version: Theory of Probability and its Applications, 1971, 16:3, 429–437

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