资料同化中非局部Zakai随机偏微分方程的有效降阶
Effective reduction for a nonlocal Zakai stochastic partial differential equation in data assimilation
摘要：
研究了一类具有振动系数的非局部随机偏微分方程的有效约化。这个随机偏微分方程中的非局部算子是非高斯Lévy过程的生成元，其跳核可以是\textbf{integrable}，也可以是\textbf{non-integrable}.我们研究这个方程的限制行为的缩放参数趋于零，并推导出一个减少（本地或非本地）的有效方程。特别是，这项工作导致一个有效的减少与Lévy噪声的数据同化系统，通过检查相应的非局部Zakai随机偏微分方程。我们表明，减少数据同化系统的概率密度近似于原系统。
英文摘要：
We study the effective reduction for a nonlocal stochastic partial differential equation with oscillating coefficients. The nonlocal operator in this stochastic partial differential equation is the generator of non-Gaussian Lévy processes, with either \textbf{integrable} or \textbf{non-integrable} jump kernels. We examine the limiting behavior of this equation as a scaling parameter tends to zero, and derive a reduced (local or nonlocal) effective equation. In particular, this work leads to an effective reduction for a data assimilation system with Lévy noise, by examining the corresponding nonlocal Zakai stochastic partial differential equation. We show that the probability density for the reduced data assimilation system approximates that for the original system.
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