Ergodic estimates of the stationary probabilities of states of a marcovian chain with continuous time

One considers the statistical characteristics of estimates of stationary probabilitiesof states of a discrete Markovian chain with continuous time in the form of the ratio of the time of staying of the chain in thisstate to the total time of observation. It is shown that this estimate is asymptotically unbiased, its asymptotic variance is determined, andthe estimate of this variance is constructed. Asymptotic normality of this estimate is proved.

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