Mixed Sub-Fractional Brownian Motion

Mounir Zili

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arXiv · 1312.3546

Mixed Sub-Fractional Brownian Motion

Mounir Zili

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Abstract

A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional Brownian motion. In this paper, we study some basic properties of this process, its non-Markovian and non-stationarity characteristics, the conditions under which it is a semimartingale, and the main features of its sample paths. We also show that this process could serve to get a good model of certain phenomena, taking not only the sign (like in the case of the sub-fractional Brownian motion), but also the strength of dependence between the increments of this phenomena into account.

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Mounir Zili. 2013-12-12. Mixed Sub-Fractional Brownian Motion. https://arxiv.org/abs/1312.3546

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