Diagnostic of the Lévy area for geophysical flow models in view of defining high order stochastic discrete-time schemes

IF 1.7 Q2 MATHEMATICS, APPLIED Foundations of data science (Springfield, Mo.) Pub Date : 2023-01-01 DOI:10.3934/fods.2023011
Pierre-Marie Boulvard, Etienne Mémin
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引用次数: 1

Abstract

In this paper we characterize numerically through two criteria the Lévy area related to unresolved fluctuation velocities associated to a stochastic coarse-scale representation of geophysical fluid flow dynamics. We study in particular whether or not the process associated to the random unresolved velocity components exhibits a Lévy area corresponding to a Wiener process, and if the law of this process can reasonably be approached by a centered Dirac measure. This exploration enables us to answer positively to a conjecture made for the constitution of high-order discrete time evolution schemes for stochastic representation defined from stochastic transport.
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基于高阶随机离散时间格式的地球物理流动模型lsamvy区域诊断
在本文中,我们通过两个标准对与地球物理流体流动动力学随机粗尺度表示相关的未解决的波动速度有关的lsamvy面积进行了数值表征。我们特别研究了与随机未解析速度分量相关的过程是否表现出与Wiener过程相对应的lsamvy区域,以及该过程的规律是否可以通过中心狄拉克测量合理地接近。这一探索使我们能够积极地回答由随机输运定义的随机表示的高阶离散时间演化方案的构造的猜想。
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