Computable Bounds for Geometric Convergence Rates of Markov Chains

Abstract

Recent results for geometrically ergodic Markov chains show that there existconstants R ! 1; ae ! 1 such thatsupjfjVjZPn(x; dy)f(y) \GammaZ?(dy)f(y)j RV (x)aenwhere ? is the invariant probability measure and V is any solution of the driftinequalitiesZP (x; dy)V (y) V (x) + b1l C (x)which are known to guarantee geometric convergence for ! 1; b ! 1 and asuitable small set C.In this paper we identify for the first time computable bounds on R and ae interms of ; b...