Computable Bounds for Geometric Convergence Rates of Markov Chains

Recent results for geometrically ergodic Markov chains show that there exist constants R < 1; < 1 such that sup jfjjV j Z P n (x; dy)f (y) Z (dy)f (y)j RV (x) n where is the invariant probability measure and V is any solution of the drift inequalities Z P (x; dy)V (y) V (x) + b1l C (x) which are known to guarantee geometric convergence for < 1; b < 1 and a suitable small set C. In this paper we identify for the rst time computable bounds on R and in terms of ; b and the minorizing constants which guarantee the smallness of C.

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