# Standardizing densities on Gaussian spaces

## TL;DR

This paper explores how to standardize random variables in infinite-dimensional Gaussian spaces, highlighting the role of Wick exponentials in the transformation of densities under specific conditions.

## Contribution

It introduces the use of Wick exponentials as a fundamental tool for standardizing densities in infinite-dimensional Gaussian spaces, a novel approach in this context.

## Key findings

- Wick exponentials are crucial for density transformations.
- Standardization procedures depend on specific conditions.
- The approach extends the understanding of Gaussian space transformations.

## Abstract

In the present note we investigate the problem of standardizing random variables taking values on infinite dimensional Gaussian spaces. In particular, we focus on the transformations induced on densities by the selected standardization procedure. We discover that, under certain conditions, the Wick exponentials are the key ingredients for treating this kind of problems.