Breuer-Major Theorems for Hilbert Space-Valued Random Variables

Marie-Christine Düker, Pavlos Zoubouloglou

Let $\{X_k{\}}_{k\in \mathbb{Z}}$ be a stationary Gaussian process with values in a separable Hilbert space ${\mathcal{H}}_1$, and let $G:{\mathcal{H}}_1\to {\mathcal{H}}_2$ be a measurable map…