We consider functional of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is α-stable Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and α-stable Lévy motion.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Fractional Brownian motion
- Long-range dependence
- Stable law