ON THE LAW OF LARGE NUMBERS FOR (GEOMETRICALLY) ERGODIC MARKOV CHAINS

Søren Tolver Jensen and Anders Rahbek

Econometric Theory, 2007, vol. 23, issue 4, 761-766

Abstract: 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.

Date: 2007
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