论文标题
超级过程的瞬时传播的特殊时间
Exceptional times for the instantaneous propagation of superprocess
论文作者
论文摘要
对于$ \ mathbb {r}^d $上的dawson-watanabe超级过程$ x $ x $ x $，在珀金斯（1990）中显示，如果基本的空间动议属于某种类似的levy流程，可以接收跳跃，那么，概率的封闭支持是$ x_t $的整个空间。传播”属性。在$ \ mathbb {r}^1 $上的SuperProcess的本文中，其空间运动是索引$α\ in（0,2/3）$的对称稳定过程，我们证明存在支持的非凡时间是紧凑和非空的。此外，我们证明了一组特殊时间是密集的，并具有完整的Hausdorff尺寸。此外，我们证明，超级进程的支持是任意集中的，因此将相应的结果（1992）从$α\ in（0,1/2）$ in（0,1/2）升级到（0,2/3）$中，我们进一步显示了这样的出色时间，也表明了一个完整的时间。
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of Lévy processes that admit jumps, then with probability one the closed support of $X_t$ is the whole space for almost all $t>0$ before extinction, the so-called ``instantaneous propagation'' property. In this paper for superprocesses on $\mathbb{R}^1$ whose spatial motion is the symmetric stable process of index $α\in (0,2/3)$, we prove that there exist exceptional times at which the support is compact and nonempty. Moreover, we show that the set of exceptional times is dense with full Hausdorff dimension. Besides, we prove that near extinction, the support of the superprocess is concentrated arbitrarily close to the distinction point, thus upgrading the corresponding results in Tribe (1992) from $α\in (0,1/2)$ to $α\in (0,2/3)$, and we further show that the set of such exceptional times also admits a full Hausdorff dimension.
