Analysis of the gradient for the stochastic fractional heat equation with spatially-colored noise in ${\mathbb{R}}^d$

Ran Wang

Consider the stochastic partial differential equation $$ \frac{\partial }{\partial t}u_t(\mathbf{x})= -(-Δ)^{\fracα{2}}u_t(\mathbf{x}) +b\left(u_t(\mathbf{x})\right)+σ\left(u_t(\ma…