Abstract: We consider the asymptotic behavior of additive functionals of linear processes with infinite variance innovations. Applying the central limit theory for Markov chains, we establish asymptotic normality for short-range dependent processes. A non-central limit theorem is obtained when the processes are long-range dependent and the innovations are in the domain of attraction of stable laws.
Key words and phrases: Central limit theorem, empirical process, level crossings, linear process, long- and short-range dependence, Markov chain, martingale, stable distribution.