Weak extinction versus global exponential growth of total mass for superdiffusions

Janos Englander, Yan-Xia Ren, Renming Song

Consider a superdiffusion $X$ on ${\mathbb{R}}^d$ corresponding to the semilinear operator $\mathcal{A}(u)=Lu+\beta u-k{u}^2,$ where $L$ is a second order elliptic operator, $\beta (\cdot )$ is in…