Effective Dynamics for a Class of Stochastic Parabolic Equation Driven by LéVy Noise With a Fast Oscillation

ABSTRACT In this paper, we mainly study the effective dynamic behavior of a class of stochastic parabolic equations driven by Lévy noise with a fast oscillation, and the coefficients of the system are assumed to satisfy the non‐Lipschitz condition. The work in the article is roughly divided into two parts. The first part, due to the change of conditions, we must consider the existence and uniqueness of the solution of the system. In the second part, we show that the original system driven by Lévy noise is reduced into an effective equation. To be more accurate, the fast component equation is averaged out, and there exists an effective process converging to the original stochastic parabolic equation. The main contribution is that the obtained results can extend the existing results from the Lipschitz condition to a weaker condition with a wider application scope, that is, the non‐Lipschitz condition, and the driving process is Lévy noise, which seems new in the existing literature.