An Extension of bifractional Brownian motion

Xavier Bardina and Khalifa Es-Sebaiy

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Spain
SAMOS-MATISSE, Centre d’Economie de La Sorbonne, Université de Paris 1 Panthéon-Sorbonne, 90, rue de Tolbiac, 75634, Paris, France.

Abstract

In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion $B^{H,K}$ with parameters $H\in~(0,1)$ and $K\in(1,2)$ such that $HK\in(0,1)$. A remarkable difference between the case $K\in(0,1)$ and our situation is that this process is a semimartingale when $2HK=1$.

Keywords: Bifractional Brownian motion, self-similar processes, long-range dependence

Published in: Communications on Stochastic Analysis, 5 (2), 333-340, 2011