Path stability of the solution of stochastic differential equation driven by time-changed L\'evy noises

TL;DR

This paper investigates the path stability of solutions to stochastic differential equations driven by time-changed Lévy noise, highlighting the influence of time drift and providing conditions for stability and exponential stability.

Contribution

It introduces new conditions for path stability of time-changed Lévy-driven SDEs and emphasizes the role of time drift in stability analysis.

Findings

Conditions for path stability and exponential stability are established.

Time drift significantly affects the stability properties.

Examples illustrate the theoretical results.

Abstract

This paper studies path stabilities of the solution to stochastic differential equations (SDE) driven by time-changed L\'evy noise. The conditions for the solution of time-changed SDE to be path stable and exponentially path stable are given. Moreover, we reveal the important role of the time drift in determining the path stability properties of the solution. Related examples are provided.