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Variations and estimators for self-similarity parameter of sub-fractional Brownian motion via Malliavin calculus

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  • Junfeng Liu
  • Donglei Tang
  • Yuquan Cang

Abstract

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of the adjusted quadratic variation for a sub-fractional Brownian motion. We apply our results to construct strongly consistent statistical estimators for the self-similarity of sub-fractional Brownian motion.

Suggested Citation

  • Junfeng Liu & Donglei Tang & Yuquan Cang, 2017. "Variations and estimators for self-similarity parameter of sub-fractional Brownian motion via Malliavin calculus," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3276-3289, April.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:7:p:3276-3289
    DOI: 10.1080/03610926.2013.819923
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