Quadratic Wiener functionals -- transformations and quadratic forms

TL;DR

This paper develops a systematic framework using Malliavin calculus to analyze quadratic Wiener functionals and their transformations, providing new insights into their Laplace transforms and revisiting prior research.

Contribution

It introduces a bi-directional relationship between quadratic Wiener functionals and transformations of order one, enhancing understanding of their structure and properties.

Findings

Established change of variables formulas on Wiener space.

Analyzed Laplace transforms of quadratic Wiener functionals.

Revisited and extended previous work with the new framework.

Abstract

Quadratic Wiener functionals are investigated systematically through transformations of order one on the Wiener space with the help of Malliavin calculus. The bi-directional relationship between quadratic Wiener functionals and transformations of order one is established via change of variables formulas on the Wiener space. The relationship is applied to the investigation of Laplace transformations of quadratic Wiener functionals. This note is made due to establishing a systematic framework to study quadratic Wiener functionals and revisiting the past works by the author with the framework.