Weak and strong averaging principle for a stochastic coupled fast–slow atmosphere–ocean model with non-Lipschitz Lévy noise. (May 2022) - Shi, Yangyang; Gao, Hongjun
Abstract: In this paper, we study the averaging principle for a stochastic coupled fast–slow atmosphere–ocean model with non-Lipschitz Lévy noise. Precisely, we will first explore the well-posedness of the model. And next, we prove regularity estimates and tightness of the slow variables. Then, we prove the ergodicity of the fast variable with the frozen slow variables. In the end, we prove that the slow variables converge to the solution of the averaged equations in probability and p th-mean ( 1 < p < 2 ), under different conditions, as time scale parameter ɛ goes to zero.