Short Communications

On the number of repetitions in Markov chains

S. A. Ivankov

Moscow

Abstract: The main result of the paper is contained in equations (4), (9) and (10) giving a uniform estimate for $|1-\exp(-x)-F_N(x)|$ where $F_N(x)$ is the distribution function of $\nu/M\nu$ and $\nu$ is the period between two successive repetitions of a given collection of the length $N$ of states of a Markov chain.

Received: 07.04.1964

 English version: Theory of Probability and its Applications, 1965, 10:3, 505–507

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