Exponential stability of second-order stochastic evolution equations with Poisson jumps

This paper is concerned with the exponential stability problem of second-order nonlinear stochastic evolution equations with Poisson jumps. By using the stochastic analysis theory, a set of novel sufficient conditions are derived for the exponential stability of mild solutions to the second-order nonlinear stochastic differential equations with infinite delay driven by Poisson jumps. An example is provided to demonstrate the effectiveness of the proposed result.

► Second-order nonlinear stochastic evolution equations with Poisson jumps and infinite delay are considered.
► A set of novel sufficient conditions for the exponential stability of mild solutions to the equations are established.
► An example is given to show the effectiveness of the obtained results.