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Symmetric weighted odd-power variations of fractional Brownian motion and applications
David Nualart, Raghid Zeineddine
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 as…
Asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time
Raghid Zeineddine
We study the asymptotic behavior of weighted power variations of fractional Brownian motion in Brownian time Z_t:= X_{Y_t}, t >= 0, where X is a fractional Brownian motion and Y is…
Change-of-variable formula for the bi-dimensional fractional Brownian motion in Brownian time
Raghid Zeineddine
Let X^{1}, X^{2} be two independent (two-sided) fractional Brownian motions having the same Hurst parameter H in (0,1), and let Y be a standard (one-sided) Brownian motion independ…
An Itô's type formula for the fractional Brownian motion in Brownian time
Ivan Nourdin, Raghid Zeineddine
Let be a (two-sided) fractional Brownian motion of Hurst parameter and let be a standard Brownian motion independent of . Fractional Brownian motion in Brow…
Fluctuations of the power variation of fractional Brownian motion in Brownian time
Raghid Zeineddine
We study the fluctuations of the power variation of fractional Brownian motion in Brownian time