## Bernoulli

• Bernoulli
• Volume 12, Number 4 (2006), 713-735.

### Power variation of some integral fractional processes

#### Abstract

We consider the asymptotic behaviour of the realized power variation of processes of the form $∫ 0 t u s dB s H$, where $B H$ is a fractional Brownian motion with Hurst parameter $H ∈(0,1)$, and $u$ is a process with finite $q$-variation, $q <1/(1-H)$. We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

#### Article information

Source
Bernoulli, Volume 12, Number 4 (2006), 713-735.

Dates
First available in Project Euclid: 16 August 2006

https://projecteuclid.org/euclid.bj/1155735933

Digital Object Identifier
doi:10.3150/bj/1155735933

Mathematical Reviews number (MathSciNet)
MR2248234

Zentralblatt MATH identifier
1130.60058

#### Citation

Manuel Corcuera, José; Nualart, David; Woerner, Jeannette H.C. Power variation of some integral fractional processes. Bernoulli 12 (2006), no. 4, 713--735. doi:10.3150/bj/1155735933. https://projecteuclid.org/euclid.bj/1155735933

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