Quantitative unique continuation for the stochastic heat equation with singular potentials

In this paper, we present a Hölder‐type quantitative assessment of unique continuation properties concerning solutions to the stochastic heat equation featuring singular potentials. We explore this phenomenon within the confines of both bounded convex domains and ‐smooth bounded domains. Our methodology draws inspiration from the frequency function method and incorporates parabolic‐type Hardy inequalities in stochastic case. Notably, these investigations, to the best of our knowledge, represent pioneering endeavors within the context of this equation.