On a discrete approximation of a skew stable L\'{e}vy process

TL;DR

This paper introduces a simplified method to approximate skew stable Lévy processes as scaling limits of perturbed standard random walks, extending the understanding of their discrete approximations.

Contribution

It provides a new, simpler construction of skew stable Lévy processes as limits of perturbed random walks, complementing previous continuous-time process approaches.

Findings

Demonstrates convergence of perturbed random walks to skew stable Lévy processes

Simplifies the construction of skew stable Lévy processes

Extends discrete approximation techniques for Lévy processes

Abstract

Iksanov and Pilipenko (2023) defined a skew stable L\'{e}vy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable L\'{e}vy processes (continuous-time processes). Here, we provide a simpler construction of the skew stable L\'{e}vy process as a scaling limit of a sequence of perturbed at $0$ standard random walks (random sequences).