On the Ergodicity of Slow-Varying Nonstationary Markov Chains
Jinn-Wen Wu, Kuo-Chih Chen · Stochastic Analysis and Applications · 2008
We consider a nonstationary Markov chain: X(k + 1) = P(k)X(k), where and P(k) is a stochastic matrix for all k = 0,1,2,…. The main purpose of this article is to present some new conditions to guarantee the ergodicity for slow-varying nonstationary Markov chains and the bound for variation of ‖P(k + 1) − P(k)‖1 to ensure the strongly ergodicity is constructed as well.