A one-dimensional non-local singular SPDE
Leandro Chiarini, Cláudio Landim · arXiv (Cornell University) · 2019
We examine in this article the one-dimensional, non-local, singular SPDE \begin{equation*} \partial_t u \;=\; -\, (-Δ)^{1/2} u \,-\, \sinh(γu) \,+\, ξ\;, \end{equation*} where $γ\in \mathbb{R}$, $(-Δ)^{1/2}$ is the fractional Laplacian of order $1/2$, $ξ$ the space-time white noise in $\mathbb{R} \times \mathbb{T}$, and $\mathbb{T}$ the one-dimensional torus. We show that for $0