Let {
X
n
}
n
≥0 be a Harris recurrent Markov chain with state space
E and invariant measure π. The law of the iterated logarithm and the law of weak convergence are given for the additive functionals
of the form
where ƒ is a real π-centered function defined on E. Some similar results are also obtained for additive functionals which are martingales associated with {X
n
}
n
≥0.
Key words and phrases: Law of the iterated logarithm – Weak convergence – Harris recurrence – Regularity
Mathematics Subject Classification (1991): 60F10, 60J10
Received: 15 September 1998 / Revised version: 1 April 1999