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2019•Physical review. ERequires access

Approximations for reflected fractional Brownian motion

Artagan Malsagov, Michel Mandjes

Open publisher page 7 citations

Abstract

Fractional Brownian motion is a widely used stochastic process that is particularly suited to model anomalous diffusion. We focus on capturing the mean and variance of fractional Brownian motion reflected at level 0. As explicit expressions or numerical techniques are not available, we base our analysis on Monte Carlo simulation. Our main findings concern closed-form approximations of the mean and variance, with a near-perfect fit.

About this research paper

What this paper is about

Fractional Brownian motion is a widely used stochastic process that is particularly suited to model anomalous diffusion. We focus on capturing the mean and variance of fractional Brownian motion reflected at level 0. As explicit expressions or numerical techniques are not available, we base our analysis on Monte Carlo simulation. Our main findings concern closed-form approximations of the mean and variance, with a near-perfect fit.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Fractional Brownian motion is a widely used stochastic process that is particularly suited to model anomalous diffusion. We focus on capturing the mean and variance of fractional Brownian motion reflected at level 0. As explicit expressions or numerical techniques are not available, we base our analysis on Monte Carlo simulation. Our main findings concern closed-form approximations of the mean and variance, with a near-perfect fit.

Key concepts: Fractional Brownian motion, Diffusion process, Geometric Brownian motion, Brownian motion, Statistical physics, Monte Carlo method, Variance (accounting), Heavy traffic approximation

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