自稳定过程
Self-stabilizing processes
摘要：
我们构造了“自稳定”过程{Z（t），t $\in [t_0,t_1)$ }.这些是随机过程，当“局部化”时，即在t附近缩放到一个精细极限时，具有$α$（Z（t））稳定过程的分布，其中$α$是R上的某个给定函数。因此，在t时的稳定性指数取决于过程在t时的值。在这里，我们解决$α$：R $\to$（0，1）的情况。首先构造了平面点集$Π$上满足一种自回归性质的确定性函数。取$Π$是一个泊松点过程，然后定义一个随机纯跳过程，我们表明有所需的本地化分布。
英文摘要：
We construct `self-stabilizing' processes {Z(t), t $\in [t_0,t_1)$}. These are random processes which when `localized', that is scaled around t to a fine limit, have the distribution of an $α$(Z(t))-stable process, where $α$ is some given function on R. Thus the stability index at t depends on the value of the process at t. Here we address the case where $α$: R $\to$ (0,1). We first construct deterministic functions which satisfy a kind of autoregressive property involving sums over a plane point set $Π$. Taking $Π$ to be a Poisson point process then defines a random pure jump process, which we show has the desired localized distributions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
