Mixed fractional Brownian motion: A spectral take

On spectral simulation of fractional Brownian motion

This paper focuses on simulating fractional Brownian motion (fBm). Despite the availability of several exact simulation methods, attention has been paid to approximate simulation (i.e., the output is approximately fBm), particularly because of possible time savings. In this paper, we study the class of approximate methods that are based on the spectral properties of fBm’s stationary incremental...

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...

Spectral correlations of fractional Brownian motion.

Fractional Brownian motion (fBm) is a ubiquitous nonstationary model for many physical processes with power-law time-averaged spectra. In this paper, we exploit the nonstationarity to derive the full spectral correlation structure of fBm. Starting from the time-varying correlation function, we derive two different time-frequency spectral correlation functions (the ambiguity function and the Kir...

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