ON THE LAW OF LARGE NUMBERS FOR (GEOMETRICALLY) ERGODIC MARKOV CHAINS
证明了对于几何遍历的马尔可夫链，强大数定律的一般形式成立，即样本均值几乎必然收敛到期望，且不依赖于初始分布，适用于非线性时间序列的渐近分析。
For use in asymptotic analysis of nonlinear time series models, we show that with (Xt,t ≥ 0) a (geometrically) ergodic Markov chain, the general version of the strong law of large numbers applies. That is, the average converges almost surely to the expectation of φ(Xt,Xt+1,…) irrespective of the choice of initial distribution of, or value of, X0. In the existing literature, the less general form has been studied.We thank Paolo Paruolo (the co-editor) and the referee for valuable comments. Also we thank the Danish Social Sciences Research Council (grant 2114-04-0001) for financial support.