Abstract:We study the spatial propagation of super-Brownian motion on $\mathbb{R}^d$ with general critical or subcritical (spatially dependent) branching mechanisms. Under local spatial lower bounds satisfying a Keller-Osserman type integrability condition, we establish a quantitative upper bound for the short-time probability that the support exits a prescribed neighborhood of its initial support. The estimate has a Gaussian-tail form and is obtained through weighted occupation times, Feynman-Kac representations, singular elliptic boundary blow-up estimates, and mild comparison arguments for log-Laplace equations. As an application, we derive the compact support property directly for spatially dependent branching mechanisms satisfying suitable local lower bounds. This yields a sufficient compact-support criterion expressed in terms of the inverse Keller integral. In particular, for spatially dependent super-Brownian motions with stable branching, we generalize the compact support results of Engländer-Pinsky and Ren.
From: Wenjing Zhang [view email]
[v1]
Tue, 2 Jun 2026 04:06:35 UTC (32 KB)
[v2]
Fri, 26 Jun 2026 08:59:59 UTC (26 KB)
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