Generalized fractional Brownian motion

TL;DR

This paper introduces a new Gaussian process that generalizes fractional and subfractional Brownian motions, exploring its properties and potential as a model for diverse natural phenomena.

Contribution

It presents a novel Gaussian process generalizing existing models, with detailed analysis of its stochastic properties and increments.

Findings

The process exhibits nonsemimartingality.

It has Hölder continuous paths.

It possesses a local time.

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, H\"{o}lder continuity, nondifferentiablity, and existence of a local time.