We study the fluctuations of the power variation of the iterated fractional Brownian motion.

Abstract. In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian motion and denoted by Γ. This process has been introduced in [16], and both its real and imaginary parts, restricted on the real axis, are usual fractional Brownian motions. The current note is devoted to prove...

In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.

The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup wil...

We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H ∈ ( 1 d+2 , 1 d ), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

1 Summary The Radon-Nikodym derivative between a centered fractional Brownian motion Z and the same process with constant drift is derived by nding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a nite interval is given. The maximum likelihood estimator of the drift and some other applications are ...

We investigate the asymptotic properties of the minimum L1-norm estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by a fractional Brownian motion.