Simulation of a Local Time Fractional Stable Motion

TL;DR

This paper presents a method to simulate sample paths of symmetric alpha-stable processes using series approximation, providing convergence rates and improving understanding of their simulation.

Contribution

It introduces a new approximation technique for symmetric alpha-stable processes and establishes convergence rates for the series simulation method.

Findings

Developed a series-based simulation method for symmetric alpha-stable processes.

Established convergence rates for the shot-noise series approximation.

Enhanced simulation accuracy for stable processes.

Abstract

In this paper, we simulate sample paths of a class of symmetric $\alpha$-stable processes using their series expression. We will develop a result in the approximation of shot-noise series. And finally, we will get a convergence rate for the approximation.