Almost periodic solutions for stochastic differential equations with Levy noise

The concept of Poisson almost periodicity is introduced. The existence and uniqueness of square-mean almost periodic solutions to some linear and semilinear stochastic differential equations with infinite dimensional Levy noise are established provided the coefficients satisfy some suitable conditions. The global asymptotic stability of the unique square-mean almost periodic solution is discussed. To illustrate the theoretical results obtained in this paper, the stochastic heat equation perturbed by both Gaussian noise and Poisson jump dependent on spatial variables is considered.