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.

Published at http://dx.doi.org/10.15559/16-VMSTA71 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

Cited by in corpus (2)

• Sojourn times of Gaussian processes with trend
• Self-similar Gaussian Markov processes