A random walk approximation to fractional Brownian motion

TL;DR

This paper introduces a novel random walk approximation for fractional Brownian motion, where the process's increments are constructed as weighted sums of past Bernoulli walk increments, enabling better modeling of long-range dependence.

Contribution

It proposes a new approximation method for fractional Brownian motion using weighted sums of Bernoulli random walk increments, bridging discrete and continuous models.

Findings

The approximation accurately captures fractional Brownian motion properties.

The method demonstrates convergence under certain conditions.

It offers a computationally feasible way to simulate fractional processes.

Abstract

We present a random walk approximation to fractional Brownian motion where the increments of the fractional random walk are defined as a weighted sum of the past increments of a Bernoulli random walk.