Heat equation with general stochastic measure colored in time

Abstract

A stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure $d\mu (t)$ is investigated in this paper. For the integrator μ, we assume the σ-additivity in probability only. The existence, uniqueness, and Hölder regularity of the solution are proved.

Keywords

• Stochastic measure
• stochastic heat equation
• mild solution
• Hölder regularity
• Besov space