# Averaging principle for the heat equation driven by a general stochastic measure

## TL;DR

This paper investigates the one-dimensional stochastic heat equation driven by a general stochastic measure, demonstrating that time averaging leads to almost sure convergence to an averaged solution.

## Contribution

It introduces a novel approach to analyze the stochastic heat equation with a broad class of stochastic measures, establishing uniform almost sure convergence results.

## Key findings

- Proves uniform almost sure convergence of the time-averaged solution
- Extends analysis to stochastic measures with only σ-additivity in probability
- Provides a framework for averaging principles in stochastic PDEs

## Abstract

We study the one-dimensional stochastic heat equation in the mild form driven by a general stochastic measure $\mu$, for $\mu$ we assume only $\sigma$-additivity in probability. The time averaging of the equation is considered, uniform a. s. convergence to the solution of the averaged equation is obtained.