Generalized fractional Brownian motion

Abstract

We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some increments characteristics. As an application, we deduce the properties of nonsemimartingality, Hölder continuity, nondifferentiablity, and existence of a local time.

Keywords

• Generalized fractional and subfractional Brownian motion
• stationarity
• Markovity
• semimartingality