Mixed sub-fractional Brownian motion

On the Mixed Fractional Brownian Motion

If H = 1/2, BH is the ordinary Brownian motion denoted by B = {Bt, t ≥ 0}. Among the properties of this process, we recall the following: (i) B 0 = 0P-almost surely; (ii) for all t ≥ 0, E((B t )2)= t2H ; (iii) the increments of BH are stationary and self-similar with order H ; (iv) the trajectories of BH are almost surely continuous and not differentiable (see [7]). Let us take a and b as two r...

Ruin Probability for Generalized Φ-sub-gaussian Fractional Brownian Motion

for various types of risk process X = (X(t), t ≥ 0) and functions f(t). The similar problem of finding the buffer overflow probability appears in the queuing theory for different communication network models. The tasks of such type were solved for many types of processes, including Gaussian ones and aforementioned FBM (see, for example, Norros [1], Michna [2], Baldi and Pacchiarotti [3], etc.)....

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.

Tempered fractional Brownian motion

Fractional Brownian motion and data

We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traac traces. We propose two extensions of fBm which come closer to actual traac traces multifractal properties.