Mixed Generalized Fractional Brownian Motion

Abstract

To extend several known centered Gaussian processes, we introduce a new centred mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the wellknown mixed fractional Brownian motion introduced by Cheridito [10] and the generalized fractional Brownian motion introduced by Zili [31]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long range dependence properties of this process.

Correlation Structure of Time-Changed Generalized Mixed Fractional Brownian Motion

“…where B = {B t , t ≥ 0} is a Bm and B H = {B H t , t ≥ 0} is an independent fBm of Hurst index H ∈ (0, 1). We refer also to [1][2][3][4] for further information on the mfBm process.…”