Published online by Cambridge University Press: 25 April 2007
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.
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