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Symmetric weighted odd-power variations of fractional Brownian motion and applications
David Nualart, Raghid Zeineddine · 2017-11-11 · via math.PR updates on arXiv.org

We prove a non-central limit theorem for the symmetric weighted odd-power variations of the fractional Brownian motion with Hurst parameter H< 1/2. As applications, we study the asymptotic behavior of the trapezoidal weighted odd-power variations of the fractional Brownian motion and the fractional Brownian motion in Brownian time Z_t:= X_{Y_t}, t >= 0, where X is a fractional Brownian motion and Y is an independent Brownian motion.

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