Strong Law of Large Numbers for branching diffusions

Janos Englander, Simon C. Harris, Andreas E. Kyprianou

Let $X$ be the branching particle diffusion corresponding to the operator $Lu+\beta (u^2-u)$ on $D\subseteq {\mathbb{R}}^d$ (where $\beta \ge 0$ and $\beta \not\equiv 0$). Let ${\lambda }_c$ denote t…