Null Controllability of a Stochastic Parabolic Equation with a Space-Dependent Analytic Noise Coefficient

We consider a stochastic parabolic equation on the $n$-dimensional flat torus $\mathbb{T}^n=(\mathbb{R}/(2π\mathbb Z))^n$, $n\in\mathbb N$, whose only control acts in the drift. The multiplicative-noise coefficient is adapted and may depend jointly on the sample point, time, and space. Its spatial p