A Karhunen-Loève theorem for random flows in Hilbert spaces

被引：0
|
作者：
Santoro, Leonardo, V [1 ]
Waghmare, Kartik G. [1 ]
Panaretos, Victor M. [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Inst Math, Lausanne, Switzerland
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2024年 / 29卷
基金：
瑞士国家科学基金会;
关键词：
Mercer's theorem; functional principal components; Hilbertian functional data; random series expansion;
D O I：
10.1214/24-ECP597
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to prove a Karhunen-Lo & egrave;ve theorem, valid for mean-square continuous random functions valued in a separable Hilbert space. That is, we establish an orthogonal series expansion with uncorrelated coefficients for second-order random flows in a Hilbert space, that holds in meansquare uniformly over time.
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页数：12
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