Extremes of vector-valued processes by finite dimensional models

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2024-08-01 DOI:10.1615/int.j.uncertaintyquantification.2024051826

Hui Xu, Mircea D. Grigoriu

引用次数: 0

Abstract

Finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables, are constructed for target vector-valued random processes/fields. They are required to have two properties. First, standard Monte Carlo algorithms can be used to generate their samples, referred to as FD samples. Second, under some conditions specified by several theorems, FD samples can be used to estimate distributions of extremes and other functionals of target random functions. Numerical illustrations involving two-dimensional random processes and apparent properties of random microstructures are presented to illustrate the implementation of FD models for these stochastic problems and show that they are accurate if the conditions of our theorems are satisfied.

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有限维模型的矢量值过程的极值

有限维（FD）模型，即时间/空间的确定性函数和随机变量的有限集，是为目标矢量值随机过程/场构建的。它们需要具备两个特性。首先，可使用标准蒙特卡罗算法生成样本，称为 FD 样本。其次，在一些定理规定的条件下，FD 样本可用于估计目标随机函数的极值分布和其他函数分布。我们给出了涉及二维随机过程和随机微结构明显特性的数值示例，以说明这些随机问题的 FD 模型的实现，并表明如果满足我们定理的条件，这些模型是准确的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.