Spectral Representation and Simulation of Fractional Brownian Motion

TL;DR

This paper introduces a novel spectral representation for fractional Brownian motion, enabling efficient simulation through algorithms based on Legendre polynomials, supported by theoretical analysis and numerical experiments.

Contribution

It presents a new spectral-based method for simulating fractional Brownian motion using Legendre polynomials, with complete algorithms and theoretical validation.

Findings

Effective spectral representation for fractional Brownian motion

Algorithms validated through numerical experiments

Enhanced simulation accuracy and efficiency

Abstract

The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the necessary algorithms and their theoretical foundation, as well as the results of numerical experiments.