3 problems

Mytnik–Xiong's persistence conjecture. The process $X$ will converge weakly, as $t\to\infty$, to some non-trivial random measure $X_\infty$ on ${\mathbb R}^d$.

Let $X'_t$ be the super Ornstein–Uhlenbeck process whose initial measure $X'_0$ is fixed and compactly supported, and consider the survival set. Let $\beta$ and $\gamma$ be the mod…

Consider the $(d,\alpha,\beta,\gamma)$-branching particle system, where $d$ is the spatial dimension, $\alpha$ is the stability parameter, $\beta$ is the branching parameter, and…