On the law of large numbers for (geometrically) ergodic Markov chains

被引：23
作者：
Tolver Jensen, Soren [1 ]
Rahbek, Anders [1 ]
机构：
[1] Univ Copenhagen, Inst Math Sci, DK-2100 Copenhagen, Denmark
来源：
ECONOMETRIC THEORY | 2007年 / 23卷 / 04期
关键词：
D O I：
10.1017/S0266466607070326
中图分类号：
F [经济];
学科分类号：
02 ;
摘要：
For use in asymptotic analysis of nonlinear time series models, we show that with (X-t, t >= 0) a (geometrically) ergodic Markov chain, the general version of the strong law of large numbers applies. That is, the average (1/T) Sigma(T-1)(t=O) phi(X-t,Xt+1,...) converges almost surely to the expectation of phi(XtXt+1,....) irrespective of the choice of initial distribution of, or value of, X-0. In the existing literature, the less general form (1/T) Sigma(T-1)(t=0) phi(X-t) has been studied.
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页码：761 / 766
页数：6
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