EXPONENTIAL STABILITY OF MATRIX-VALUED MARKOV CHAINS VIA NONIGNORABLE PERIODIC DATA
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2017 American Mathematical Society. Let = {n} n0 be a Markov chain defined on a probability space (, F, P) valued in a discrete topological space S that consists of a finite number of real d d matrices. As usual, is called uniformly exponentially stable if there exist two constants C > 0 and 0 < < 1 such that (Formula Presented) and is called nonuniformly exponentially stable if there exist two random variables C() > 0 and 0 < () < 1 such that (Formula Presented) In this paper, we characterize the exponential stabilities of via its nonignorable periodic data whenever has a constant transition binary matrix. As an application, we construct a Lipschitz continuous SL(2, R)-cocycle driven by a Markov chain with 2-points state space, which is nonuniformly but not uniformly hyperbolic and which has constant Oselede splitting with respect to a canonical Markov measure.