Central limit theorem for periodic solutions of stochastic differential equations driven by Levy noise

Abstract

Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and periodic transition semigroup. Under suitable conditions, we also achieve a certain contractivity in the space of probability measures. By constructing an appropriate invariant measure, we standardize the observation functions. Utilizing the classical martingale approximation approach, we establish the law of large numbers and the central limit theorem.