Lyapunov-type conditions and stochastic differential equations driven by GG-Brownian motion

This paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the solution for locally Lipschitz GSDEs is obtained by localization methods, also the stability of such GSDEs are discussed with Lyapunov-type conditions

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

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.Comment: arXiv admin note: substantial text overlap with arXiv:1211.2973 by other author