随机紧集的紧性准则
Tightness criteria for random compact sets of cadlag paths
AI总结：
本文基于Skorohod J1和M1拓扑给出随机变量在cadlag路径紧集空间中的紧性准则，扩展了连续路径研究中的早期工作，并通过重标定厚尾泊松树和织物应用验证了非交叉路径的弱极限点非交叉性。
摘要：
我们基于Skorohod J1和M1拓扑给出随机变量在所有cadlag实值路径紧集空间中的紧性准则。这扩展了早期工作，该工作受布朗运动网络研究启发，仅关注连续路径。在M1情况下，我们给出紧性准则的自然扩展，确保非交叉路径系统具有非交叉的弱极限点。此结果通过厚尾泊松树的重标定和更一般性的织物应用进行了示例。
英文摘要：
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This extends earlier work motivated by the study of the Brownian web that was concerned only with continuous paths. In the M1 case, we give a natural extension of our tightness criteria which ensures that non-crossing systems of paths have weak limit points that are also non-crossing. This last result is exemplified through a rescaling of heavy tailed Poisson trees and a more general application to weaves.
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。
