Publication

A Karhunen–Loève theorem for random flows in Hilbert spaces

Victor Panaretos, Leonardo Vincenzo Santoro, Kartik Waghmare
2024

Abstract

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-Loève 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 mean-square uniformly over time.

Official source

https://infoscience.epfl.ch/entities/publication/aa845b6d-1782-4687-9abe-821cadd6d43e

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

A Karhunen–Loève theorem for random flows in Hilbert spaces

Chat with Graph Search

THE POSITIVE-DEFINITE COMPLETION PROBLEM

Binary Maximal Leakage

Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks