Nonstandard limit theorem for infinite variance functionals

Allan Sly, Chris Heyde

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)796-805
Number of pages10
JournalAnnals of Probability
Issue number2
StatePublished - Mar 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Fractional Brownian motion
  • Hyper-contractivity
  • Long-range dependence
  • Stable law


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