Approximation and stability of solutions of SDEs driven by a symmetric \alpha\ stable process with non-Lipschitz coefficients

TL;DR

This paper studies the approximation and stability of solutions to SDEs driven by symmetric ble stable processes, focusing on non-Lipschitz coefficients and establishing conditions for strong solutions and their stability.

Contribution

It introduces Euler-Maruyama approximation for such SDEs under Komatsu condition and analyzes solution stability under multiple coefficient conditions.

Findings

Euler-Maruyama approximation ensures existence of strong solutions.

Stability of solutions is established under Komatsu and Belfadli-Ouknine conditions.

Provides theoretical insights into SDEs driven by ble stable processes with non-Lipschitz coefficients.

Abstract

Firstly, we investigate Euler-Maruyama approximation for solutions of stochastic differential equations (SDEs) driven by a symmetric \alpha\ stable process under Komatsu condition for coefficients. The approximation implies naturally the existence of strong solutions. Secondly, we study the stability of solutions under Komatsu condition, and also discuss it under Belfadli-Ouknine condition.