# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1704.02103