Lévy环境下竞争CB-过程的灭绝与从无穷大下降
Extinction and coming down from infinity of CB-processes with competition in a Lévy environment
摘要：
本文研究了在Lévy环境中具有竞争的连续态分支（简称CB）过程的灭绝事件和从无穷远下降的性质，其中的分支机制满足所谓的Grey条件.特别地，我们在假设Lévy环境不向无穷大漂移的情况下推导出，对于任何起始点，过程在有限时间a.s.内灭绝。此外，如果我们对竞争机制施加一个可积性条件，那么无论环境的长期行为如何，这个过程都是从无穷大开始的。
英文摘要：
In this note, we are interested on the event of extinction and the property of coming down from infinity of continuous state branching (or CB for short) processes with competition in a Lévy environment whose branching mechanism satisfies the so-called Grey's condition. In particular, we deduce, under the assumption that the Lévy environment does not drift towards infinity, that for any starting point the process becomes extinct in finite time a.s. Moreover if we impose an integrability condition on the competition mechanism, then the process comes down from infinity regardless the long term behaviour of the environment.
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