The Gaussian Radon Transform in Classical Wiener Space

TL;DR

This paper investigates the Gaussian Radon transform within classical Wiener space, providing explicit formulas for Brownian functionals and establishing a Fock space decomposition for conditioned Gaussian measures.

Contribution

It introduces explicit formulas for the Gaussian Radon transform of Brownian functionals and develops a Fock space decomposition for conditioned Gaussian measures.

Findings

Explicit formulas for the Gaussian Radon transform of Brownian functionals

Fock space decomposition for Gaussian measures conditioned on affine subspaces

Enhanced understanding of Gaussian measures in Wiener space

Abstract

We study the Gaussian Radon transform in the classical Wiener space of Brownian motion. We determine explicit formulas for transforms of Brownian functionals specified by stochastic integrals. A Fock space decomposition is also established for Gaussian measure conditioned to closed affine subspaces in Hilbert spaces.