Central limit theorem for centered frequencies of a countable ergodic markov chain

  • N. V. Moskal'tsova
  • V. M. Shurenkov

Abstract

On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state.
Published
25.12.1993
How to Cite
Moskal’tsovaN. V., and ShurenkovV. M. “Central Limit Theorem for Centered Frequencies of a Countable Ergodic Markov Chain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 12, Dec. 1993, pp. 1713–1715, https://umj.imath.kiev.ua/index.php/umj/article/view/5982.
Section
Short communications