Central Limit Theorem and Moderate deviation for nonhomogenenous Markov chains

Mingzhou Xu, Yunzheng Ding, Yongzheng Zhou

Published 2020-10-14Version 1

Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore, we obtain a corresponding moderate deviation theorem for countable nonhomogeneous Markov chain by G\"artner-Ellis theorem and exponential equivalent method.