Abstract:We consider the local times of $(1+\beta)$-stable $d$-dimensional super-Brownian motion with $0<\beta<1$. Mytnik and Perkins (2003) proved that the local time, denoted by $L(t, x)$, is jointly continuous for $d=1$, whereas it is locally unbounded in $x$ for $d\geq 2$ where it exists. This paper strengthens the results of Mytnik and Perkins for $d=1$ by showing that when $X_0$ is atomless, $L(t,\cdot)$ is differentiable at every fixed deterministic point almost surely and is differentiable Lebesgue-a.e. However, with probability one, the local time is almost surely not differentiable at every spatial point simultaneously.
From: Jieliang Hong [view email]
[v1]
Fri, 26 Sep 2025 08:14:00 UTC (24 KB)
[v2]
Wed, 19 Aug 2026 07:57:13 UTC (16 KB)
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