Regular Transformation Groups Based on Fourier-Gauss Transforms

TL;DR

This paper explores new representations of White noise spaces using generalized Wick tensors and extends the Mehler formula for the Ornstein-Uhlenbeck semigroup, enhancing understanding of stochastic analysis.

Contribution

Introduces generalized Wick tensors for White noise spaces and generalizes the Mehler formula for the Ornstein-Uhlenbeck semigroup.

Findings

New representations of White noise spaces using generalized Wick tensors

Generalized Mehler formula for Ornstein-Uhlenbeck semigroup

Enhanced tools for stochastic analysis and white noise theory

Abstract

We discuss different representations of the White noise spaces $(E)_{\beta}$, $0 \leq \beta < 1$ by introducing generalized Wick tensors. As an application we state a generalization of the Mehler formula for the Ornstein-Uhlenbeck semigroup.