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
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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 -