Finite dimensional models for random microstructures

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2022-05-16 DOI:10.1090/tpms/1168
M. Grigoriu
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FD models of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z left-parenthesis x right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>Z</mml:mi>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mi>x</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">Z(x)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> and <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U left-parenthesis x right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>U</mml:mi>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mi>x</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">U(x)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> constitute surrogates of these random fields which target various properties, e.g., mean/correlation functions or sample properties. 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引用次数: 3

Abstract

Finite dimensional (FD) models, i.e., deterministic functions of space depending on finite sets of random variables, are used extensively in applications to generate samples of random fields Z ( x ) Z(x) and construct approximations of solutions U ( x ) U(x) of ordinary or partial differential equations whose random coefficients depend on Z ( x ) Z(x) . FD models of Z ( x ) Z(x) and U ( x ) U(x) constitute surrogates of these random fields which target various properties, e.g., mean/correlation functions or sample properties. We establish conditions under which samples of FD models can be used as substitutes for samples of Z ( x ) Z(x) and U ( x ) U(x) for two types of random fields Z ( x ) Z(x) and a simple stochastic equation. Some of these conditions are illustrated by numerical examples.

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随机微观结构的有限维模型
有限维(FD)模型,即取决于随机变量的有限集合的空间的确定性函数,在应用中被广泛地用于生成随机场Z(x)Z(x)的样本,并构造其随机系数取决于Z(x。Z(x)Z(x)和U(x)U(x)的FD模型构成了这些随机场的替代物,这些随机场以各种性质为目标,例如,均值/相关函数或样本性质。我们建立了FD模型的样本可以用作两种类型的随机场Z(x)Z(x)和一个简单随机方程的Z(x,Z(x,Z)和U(x)U(x)样本的替代品的条件。其中一些条件通过数值例子加以说明。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
22
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