4 papers · 1 filter
Breuer-Major Theorems for Hilbert Space-Valued Random Variables
Marie-Christine Düker, Pavlos Zoubouloglou
Let be a stationary Gaussian process with values in a separable Hilbert space , and let be a measurable…
On extremes for Gaussian subordination
Shuyang Bai, Marie-Christine Duker
This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The m…
The Fourth-Moment Theorem on Hilbert Spaces
Marie-Christine Düker, Pavlos Zoubouloglou
In this work, we establish conditions ensuring convergence in distribution of a sequence admitting a Wiener-Itô chaos representation to a nondegenerate Gaussian measure on a separ…
Scaling limits for sample autocovariance operators of Hilbert space-valued linear processes
Marie-Christine Düker, Pavlos Zoubouloglou
This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at dif…