Exponential Stability of Solutions to Stochastic Differential Equations Driven by G-Levy Process

TL;DR

This paper establishes stability criteria for solutions to stochastic differential equations driven by G-Levy processes, using G-Lyapunov functions, and introduces a BDG-type inequality in G-stochastic calculus.

Contribution

It introduces a BDG-type inequality for G-stochastic calculus with G-Levy processes and constructs solutions under non-Lipschitz conditions, analyzing their stability.

Findings

Established BDG-type inequality for G-stochastic calculus

Constructed solutions under non-Lipschitz conditions

Proved mean square and quasi sure exponential stability

Abstract

In this paper, BDG-type inequality for G-stochastic calculus with respect to G-Levy process is obtained and solutions of stochastic differential equations driven by G-Levy process under non-Lipschitz condition are constructed. Moreover, we establish the mean square exponential stability and quasi sure exponential stability of the solutions be means of G-Lyapunov function method. An example is presented to illustrate the efficiency of the obtained results.