The stability with general decay rate of neutral stochastic functional hybrid differential equations with Levy noise

摘要

This paper is concerned with the existence and uniqueness, the almost sure stability with general decay rate (including almost sure exponential stability, almost sure polynomial stability and almost sure logarithmic stability) for the global solution of nonlinear neutral stochastic functional hybrid differential equations with Levy noise. The key technique used is the method of Lyapunov function, nonnegative semi-martingale convergence theorem and the theory of M-matrix. We use auxiliary functions to dominate the corresponding Lyapunov function and the diffusion operator. Our conditions on the diffusion operator are weaker than those in the related existing works. Finally, one example is given to show the effectiveness of the obtained theory. (C) 2020 Elsevier B.V. All rights reserved.