Weak convergence of the complex fractional Brownian motion

Weak convergence to the fractional Brownian sheet in Besov spaces

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent...

Convergence of weighted power variations of fractional Brownian motion

The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion B with Hurst index H ∈ (0, 1). The behaviour is different when H < 1/2 and powers are odd, compared with the case when H = 1/2 or when H > 1/2 and powers are even. In the second part, one applies the results of the first part to compute the exact rate of convergen...

Convergence of Scaled Renewal Processes to Fractional Brownian Motion

The superposition process of independent counting renewal processes associated with a heavy-tailed interarrival time distribution is shown to converge weakly after rescaling in time and space to fractional Brownian motion, as the number of renewal processes tends to innnity. Corresponding results for continuous arrival uid processes are discussed.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.