带乘性α-稳定噪声的多尺度非齐次时间SDE的强平均原理
Strong averaging principle for multiscale time-inhomogeneous SDEs with multiplicative $α$-stable noises
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中文总结 AI 辅助
本文针对乘性α-稳定噪声驱动的多尺度非齐次时间随机系统，基于Khasminskii离散化方法建立强平均原理，证明慢子系统向两类平均系统的强收敛性，并将结果应用于气候-天气系统。
中文摘要 AI 辅助
本文研究由α∈(1,2)的乘性α-稳定过程驱动的多尺度非齐次时间随机系统的强平均原理。基于Khasminskii离散化方法，我们首先建立冻结慢变量的快分量过程具有周期测度；接着证明慢子系统对依赖于时间尺度ε的平均系统的强收敛性。对任意固定ε，若两个周期τ₁和ετ₂的倒数是有理线性无关的，一个重要结论是该平均系统具有随机拟周期性。此外，通过应用遍历定理，我们证明慢子系统对另一个不依赖时间尺度ε的非齐次时间SDE平均系统的强收敛性。即使在乘性α-稳定噪声的完全耦合多尺度系统的时间齐次情形下，我们的结果也是新颖的。最后，我们将该结果应用于气候-天气系统。
英文摘要
In this paper, we study the strong averaging principle for multiscale time-inhomogeneous stochastic systems driven by multiplicative $α$-stable processes with $α\in(1,2)$. Based on Khasminskii's discretization approach, we first establish that the fast component processes with a frozen slow variable admits a periodic measure. We then prove the strong convergence of the slow subsystem to an averaged system that depends on the time scale $\varepsilon$. For any fixed $\varepsilon$, if the reciprocals of the two periods $τ_1$ and $\varepsilon τ_2$ are rationally linearly independent, an important consequence is that the averaged system has random quasi-periodicity. Furthermore, by applying the ergodic theorem, we prove the strong convergence of the slow subsystem to another averaged system, a time-inhomogeneous SDEs independent of the time scale $\varepsilon$. Our result is also novel even in the time-homogeneous case for a fully coupled multiscale system with multiplicative $α$-stable noises. Finally, we apply the result to a climate-weather system.
