The \(p\)th moment exponential stability and almost surely exponential stability of stochastic differential delay equations with Poisson jump
In this paper the authors study a class of nonlinear stochastic differential delay equations with Poisson jump. By means of a Lyapunov function and the semi-martingale convergence theorem, they first prove the existence and uniqueness of a global solution under a local Lipschitz condition and a new nonlinear growth condition. Then some sufficient conditions ensuring the \(p\)-th moment and almost sure stability are established.
nonlinear stochastic differential delay equation
scientific article; zbMATH DE number 6996177