TRANSIENCE AND INVARIANT FUNCTIONS FOR MARKOV CHAINS IN DOUBLY INFINITE RANDOM ENVIRONMENT
Yingqiu Li · Chinese Annals of Mathematics,series A · 2003
In investigate field of Markov chains in random environments, the concepts for π-irreduciblity, recurrence and transience of Markov chains in doubly infinite random environment are introduced. The sufficient and necessary conditions that π-irreducible Markov chains in doubly infinite random environment are transient is given. The concepts for invariant functions of Markov chains in doubly infinite random environment are introduced. Their existence and basic properties are studied. Using these properties, a criterion that π-irreducible Markov chains in doubly infinite random environment are transient is given.