A0820
Title: Breuer-Major theorems for Hilbert space-valued random variables
Authors: Marie Duker - FAU Erlangen (Germany) [presenting]
Abstract: Nonlinear functionals of Gaussian random variables, also called Gaussian subordinated variables, provide a flexible model in time series analysis. Under suitable conditions on the functionals and the correlation structure of the latent Gaussian variables, one can derive a central limit theorem (CLT). The concept of Gaussian subordination is studied in general Hilbert spaces, allowing the latent Gaussian variables and the functions to take values in suitable Hilbert spaces. To prove a CLT for Hilbert space-valued subordinated processes, techniques are employed from Malliavin calculus, a powerful tool in modern stochastic analysis. In a series of examples, the derived CLT is emphasized to recover limit theorems for a wide array of statistics relevant to functional data analysis and present novel applications to the theory of operator neural networks.
