# Integration-by-Parts Characterizations of Gaussian Processes

## TL;DR

This paper extends the integration-by-parts framework from Malliavin calculus to characterize Gaussian Fredholm processes, broadening the tools for stochastic analysis of Gaussian processes.

## Contribution

It introduces a new integration-by-parts characterization for Gaussian Fredholm processes, expanding the scope of stochastic analysis techniques.

## Key findings

- Characterization of Gaussian Fredholm processes via integration-by-parts
- Extension of Malliavin calculus tools to a broader class of Gaussian processes
- Potential applications in stochastic analysis and modeling

## Abstract

The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts formula also characterizes a wide class of Gaussian processes, the so-called Gaussian Fredholm processes.