THE GENERALIZED BIFRACTIONAL BROWNIAN MOTION

Abstract

To extend several known centered Gaussian processes, we introduce a new centered Gaussian process, named the generalized bifractional Brownian motion. This process depends on several parameters, namely α > 0 , β>0 , 0<H<1 and 0<K≤1 . When K=1, we investigate its convexity properties. Then, when 2HK≤ 1, we prove that this process is an element of the QHASI class, a class of centered Gaussian processes, which was introduced in 2015