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- W1985871343 abstract "In this paper, we consider time-homogeneous and asymptotically space-homogeneous Markov chains that take values on the real line and have an invariant measure. Such a measure always exists if the chain is ergodic. In this paper, we continue the study of the asymptotic properties of $pi([x,infty))$ as $x rightarrow infty$ for the invariant measure $pi$, which was started in [A. A. Borovkov,Stochastic Processes in Queueing Theory, Springer-Verlag, New York, 1976], [A. A. Borovkov, Ergodicity and Stability of Stochastic Processes, TVP Science Publishers, Moscow, to appear], and [A. A. Brovkov and D. Korshunov, Ergodicity in a sense of weak convergence, equilibrium-type identities and large deviations for Markov chains, in Probability Theory and Mathematical Statistics, Coronet Books, Philadelphia, 1984, pp. 89--98]. In those papers, we studied basically situations that lead to a purely exponential decrease of $pi([x,infty))$. Now we consider two remaining alternative variants: the case of power decr..." @default.
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- W1985871343 date "1997-01-01" @default.
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- W1985871343 title "Large-Deviation Probabilities for One-Dimensional Markov ChainsPart 1: Stationary Distributions" @default.
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- W1985871343 doi "https://doi.org/10.1137/tprbau000041000001000001000001" @default.
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