Lévy 环境下带竞争的连续状态分支过程的灭绝与从无穷下落
概率论
2019-06-05 v3
摘要
在本注记中，我们关注分支机制满足所谓 Grey 条件的 Lévy 环境下带竞争的连续状态分支（简称 CB）过程的灭绝事件与从无穷下落性质。特别地，我们推导出，在 Lévy 环境不向无穷漂移的假设下，对于任意起点，该过程在有限时间内几乎必然灭绝。此外，若对竞争机制施加一个可积性条件，则无论环境的长期行为如何，该过程都会从无穷下落。
引用
@article{arxiv.1801.04501,
title = {Extinction and coming down from infinity of CB-processes with competition in a L\'evy environment},
author = {Hélène Leman and Juan Carlos Pardo},
journal= {arXiv preprint arXiv:1801.04501},
year = {2019}
}
备注
Changes with respect to v2: Due to its length, the paper was cut in half, this version gathers the results concerning CSBP with general competition in a L\'evy random environment. Firstly, the results were improved and secondly, results concerning coming down from infinity of the process were added. The second part of the paper is given in a separated preprint