# Chung's Law of the Iterated Logarithm for a Class of Stochastic Heat Equations

## TL;DR

This paper proves a Chung-type law of the iterated logarithm for solutions to certain stochastic heat equations with multiplicative noise, extending classical results beyond Gaussian cases.

## Contribution

It establishes a Chung's law of the iterated logarithm for stochastic heat equations with solution-dependent noise, using small ball probabilities and freezing coefficient techniques.

## Key findings

- Limiting constant in Chung's law can be evaluated almost surely.
- Results extend classical laws to non-Gaussian stochastic heat equations.
- Provides a new approach for analyzing stochastic PDEs with multiplicative noise.

## Abstract

We establish a Chung-type law of the iterated logarithm for the solutions of a class of stochastic heat equations driven by a multiplicative noise whose coefficient depends on the solution, and this dependence takes us away from Gaussian setting. Based on the literature on small ball probabilities and the technique of freezing coefficients, the limiting constant in Chung's law of the iterated logarithm can be evaluated almost surely.