# Prediction Law of Mixed Gaussian Volterra Processes

## TL;DR

This paper investigates the prediction of mixed Gaussian Volterra processes with noisy observations, providing insights into their conditional laws and applications in variance reduction under measurement errors.

## Contribution

It introduces a novel analysis of the regular conditional law for Gaussian Volterra processes with noisy inputs, extending prediction methods under model disturbances.

## Key findings

- Derived the conditional law of mixed Gaussian Volterra processes with noisy observations.
- Applied the results to improve variance reduction techniques in measurement error scenarios.
- Provided theoretical foundations for predicting unobservable processes in noisy environments.

## Abstract

We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra processes driven by a Brownian motion in a case where the Brownian motion is not observable, but only a noisy version is observed. As an application, we discuss how our result can be applied to variance reduction in the presence of measurement errors.