# Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution

## TL;DR

This paper studies the stochastic heat equation with space-only Gaussian white noise in one dimension, revealing that the regularity of solutions is consistent for both additive and multiplicative noise under Wick-Itô-Skorokhod interpretation.

## Contribution

It provides a detailed analysis of the regularity of solutions to the heat equation with space-only Gaussian white noise, a case less explored in existing literature.

## Key findings

- Solution regularity is identical for additive and multiplicative noise.
- The study focuses on the Wick-Itô-Skorokhod interpretation.
- Addresses a gap in understanding the heat equation with space-only white noise.

## Abstract

Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive the attention it deserves. The paper investigates the stochastic heat equation with space-only Gaussian white noise on a bounded interval. The main result is that the space-time regularity of the solution is the same for additive noise and for multiplicative noise in the Wick-It\^o-Skorokhod interpretation.