The Invariance Principle for p- $$ \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{\theta } $$ Chain

Abstract

There are two parts in this paper. In the first part we construct the Markov chain in random environment (MCRE), the skew product Markov chain and p–\( \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{\theta } \) chain from a random transition matrix and a two–dimensional probability distribution, and in the second part we prove that the invariance principle for p–\( \ifmmode\expandafter\vec\else\expandafter\vecabove\fi{\theta } \) chain, a more complex non–homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.