Let denote the -th partial sum of a sequence of random variables, and let . When are independent identically distributed bounded nonlattice random variables satisfying and , D. Iglehart [Ann. Math. Stat. 43, 627-635 (1972; Zbl 0238.60072)] proved that has a limiting double exponential distribution, where satisfies . In the present paper the authors obtain a similar result for a sequence satisfying the following conditions:
(i) are conditionally independent given a finite state irreducible aperiodic Markov chain ,
(ii) the conditional distribution of given depends only on the two states and .