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

TL;DR

This paper proves the existence of periodic solutions and establishes a central limit theorem for stochastic differential equations driven by Levy noise, with implications for invariant measures and probabilistic convergence.

Contribution

It introduces a method to obtain periodic solutions and a CLT for infinite-dimensional Levy-driven SDEs, extending classical results to this complex setting.

Findings

Existence of periodic solutions in distribution

Construction of periodic measures and transition semigroup

Law of large numbers and CLT for the system

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.