Information on the seminar the Wiener chaos decomposition and (non-)central limit theorems

Assistant:

Date: Tue, 2-4 p.m., SR 127, Ernst-Zermelo-Str. 1

Preliminary discussions: Information will follow!

Language: Lectures/participation in German or English possible

Current

Content

It is a well-established fact that linear transformations of Gaussian processes preserve their Gaussian property. However, this is generally not true for non-linear transformations such as for general additive functionals. The Wiener chaos decomposition provides a framework for analyzing non-linear functionals of Gaussian processes. Elements of some Wiener chaos can be represented as multiple Wiener-Itô integrals. The concept of Wiener chaos generalizes the properties of orthogonal polynomials on the real line to an infinite dimensional setting.

In this seminar, we will explore the fundamental properties of Wiener chaos, beginning with the Hermite polynomial basis, which serves as orthogonal decomposition framework for representing such random processes. Following this, we will examine advanced topics, including applications to Malliavin calculus, central and noncentral limit theorems for non-linear functionals of Gaussian and non-Gaussian fields, and invariance principles.

List of lecture topics

Literature

Previous knowledge

Usability

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Consultation hour

Lecturer consultation hours: Di, 16-17 Uhr
Consultation hour assistant: