Kavli Affiliate: Ran Wang | First 5 Authors: Ran Wang, , , , | Summary: Consider the stochastic partial differential equation $$ frac{partial }{partial t}u_t(mathbf{x})= -(-Delta)^{frac{alpha}{2}}u_t(mathbf{x}) +bleft(u_t(mathbf{x})right)+sigmaleft(u_t(mathbf{x})right) dot F(t, mathbf{x}), tge0, mathbf{x}in mathbb R^d, $$ where $-(-Delta)^{frac{alpha}{2}}$ denotes the fractional Laplacian with the power $alpha/2in (1/2,1]$, and the driving noise $dot F$ is a centered […]
Continue.. Analysis of the gradient for the stochastic fractional heat equation with spatially-colored noise in $mathbb R^d$