Some Fractional and Multifractional Gaussian Processes: A Brief Introduction

TL;DR

This paper introduces various fractional and multifractional Gaussian processes, highlighting their mathematical properties and potential applications in modeling complex natural and engineered systems.

Contribution

It provides a concise overview of key fractional and multifractional Gaussian processes, emphasizing their importance and usage in modeling real-world phenomena.

Findings

Overview of fractional Brownian motion types

Introduction to multifractional processes

Discussion of applications in modeling natural phenomena

Abstract

This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifrac- tional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.