TY - JOUR

T1 - Rates of convergence for everywhere-positive Markov chains

AU - Baxter, J. R.

AU - Rosenthal, Jeffrey S.

PY - 1995/3

Y1 - 1995/3

N2 - We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

AB - We generalize and simplify a result of Schervish and Carlin (1992) concerning the convergence of Markov chains to their stationary distributions. We prove geometric convergence for any Markov chain whose transition operator is compact and has everywhere-positive density functions (with respect to some reference measure). We also provide, without requiring compactness, a quantitative estimate of the convergence rate, given in terms of the stationary distribution.

KW - Compact operator

KW - Geometric convergence

KW - Gibbs sampler

KW - Hilbert-Schmidt condition

KW - Markov chain

KW - Monte Carlo

KW - Stationary distribution

UR - http://www.scopus.com/inward/record.url?scp=0000178531&partnerID=8YFLogxK

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U2 - 10.1016/0167-7152(94)00085-M

DO - 10.1016/0167-7152(94)00085-M

M3 - Article

AN - SCOPUS:0000178531

VL - 22

SP - 333

EP - 338

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 4

ER -