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.