Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data

Xinping Gui, Buyang Li, Jilu Wang

A class of stochastic Besov spaces $B^p{L}^2(\Omega ;{\dot{H}}^{\alpha }(\mathcal{O}))$, $1\le p\le \infty$ and $\alpha \in [-2,2]$, is introduced to characterize the regularity of the noise in the semiline…