On stochastic heat equation with measure initial data

TL;DR

This paper establishes existence, uniqueness, and moment bounds for solutions to a stochastic heat equation with measure initial data, avoiding iterative methods used in prior works.

Contribution

It provides a new approach to analyze stochastic heat equations with measure initial data without relying on iteration techniques.

Findings

Proved existence and uniqueness of solutions.

Derived upper bounds for moments of the solution.

Avoided the use of iterative methods in the analysis.

Abstract

The aim of this short note is to obtain the existence, uniqueness and moment upper bounds of the solution to a stochastic heat equation with measure initial data, without using the iteration method in Chen and Dalang(2015), Chen and Kim(2016).