Heat equation with a general stochastic measure in a bounded domain

Abstract

A stochastic heat equation on $[0,T]\times B$, where B is a bounded domain, is considered. The equation is driven by a general stochastic measure, for which only σ-additivity in probability is assumed. The existence, uniqueness and Hölder regularity of the solution are proved.

Keywords

• Heat equation
• mild solution
• Stochastic measure
• Hölder regularity