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Computable bounds for geometric convergence rates of Markov chains
, 1994
"... Recent results for geometrically ergodic Markov chains show that there exist constants R ! 1; ae ! 1 such that sup jfjV j Z P n (x; dy)f(y) \Gamma Z ß(dy)f(y)j RV (x)ae n where ß is the invariant probability measure and V is any solution of the drift inequalities Z P (x; dy)V (y) V (x) ..."
Abstract

Cited by 66 (6 self)
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Recent results for geometrically ergodic Markov chains show that there exist constants R ! 1; ae ! 1 such that sup jfjV j Z P n (x; dy)f(y) \Gamma Z ß(dy)f(y)j RV (x)ae n where ß 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 first time computable bounds on R and ae in terms of ; b and the minorizing constants which guarantee the smallness of C. In the simplest case where C is an atom ff with P (ff; ff) ffi we can choose any ae ? # where [1 \Gamma #] \Gamma1 = 1 (1 \Gamma ) 2 h 1 \Gamma + b + b 2 + i ff (b(1 \Gamma ) + b 2 ) i and i ff i 34 \Gamma 8ffi 2 ffi 3 ji b 1 \Gamma j 2 ; and we can then choose R ae=[ae \Gamma #]. The bounds for general small sets C are similar but more complex. We apply these to simple queueing models and Markov chain Mo...
Perfect Sampling From Independent MetropolisHastings Chains
 Journal of Statistical Planning and Inference
, 2002
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Singular limits of Schrödinger operators and Markov processes
 J. OPERATOR THEORY
, 1999
"... After introducing the Γconvergence of a family of symmetric matrices, we study the limits in that sense, of Schrödinger operators on a finite graph. The main result is that any such limit can be interpreted as a Schrödinger operator on a new graph, the construction of which is described explicitly ..."
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Cited by 4 (2 self)
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After introducing the Γconvergence of a family of symmetric matrices, we study the limits in that sense, of Schrödinger operators on a finite graph. The main result is that any such limit can be interpreted as a Schrödinger operator on a new graph, the construction of which is described explicitly. The operators to which the construction is applied are reversible, almost reducible Markov generators. An explicit method for computing an equivalent of the spectrum is described. Among possible applications, quasidecomposable processes and lowtemperature simulated annealing are studied.
Z (dy)f(y)j RV (x)
, 1995
"... Recent results for geometrically ergodic Markov chains show that there exist constants R <1; < 1 such that sup jf jV j Z ..."
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Recent results for geometrically ergodic Markov chains show that there exist constants R <1; < 1 such that sup jf jV j Z