论文标题
出口措施，当地时间和超级棕色运动的当地时间
Exit measure, local time and a boundary local time of super-Brownian motion
论文作者
论文摘要
我们从一个小球的补充中使用$ x \ in \ mathbb {r}^d $ in \ mathbb {r}^d $ in \ d \ leq 3 $的补充，以$ x $ $ x $的$ x $ l^x $的超级l^x $的新结构，以$ x $ $ x $进行新的构造。在\ cite {hong20}中，集中在$ x $上的出口量度的总质量更为单一的重新归一化，其中出口量度为正，但异常小，用于建立一个在超级棕色运动范围的拓扑边界上支撑的边界当地时间。我们的出口量度构建$ l^x $激发了这种翻新。我们通过确定相关的平均度量对明确限制的融合来在这里赋予这一构造的重要一步；这将用于在\ cite {hong20}中构建边界当地时间。我们的两种结果都取决于解决方案对相关的半椭圆方程的行为，并具有单数初始数据，以及Le Gall的特殊Markov属性以进行退出措施。
We use a renormalization of the total mass of the exit measure from the complement of a small ball centered at $x\in \mathbb{R}^d$ for $d\leq 3$ to give a new construction of the total local time $L^x$ of super-Brownian motion at $x$. In \cite{Hong20} a more singular renormalization of the total mass of the exit measure concentrating on $x$, where the exit measure is positive but unusually small, is used to build a boundary local time supported on the topological boundary of the range of super-Brownian motion. Our exit measure construction of $L^x$ motivates this renormalization. We give an important step of this construction here by establishing the convergence of the associated mean measure to an explicit limit; this will be used in the construction of the boundary local time in \cite{Hong20}. Both our results rely on the behaviour of solutions to the associated semilnear elliptic equation with singular initial data and on Le Gall's special Markov property for exit measures.
