论文标题
某些强烈从属的莱维过程需要弱从属
Necessity of weak subordination for some strongly subordinated Lévy processes
论文作者
论文摘要
考虑使用多元下属的多元Lévy过程的强大从属。如果下属是一堆独立的lévy过程，并且下属的组成部分在每个堆栈中都无法区分，那么强的下属会产生一个lévy的过程，否则可能不会。引入了弱的从属，以扩展强大的从属，即使没有强大的从属量也没有产生莱维过程。在这里，我们证明在上述条件下，强度和弱的从属法在法律上是平等的。此外，我们证明，如果强大的从属是一个莱维过程，那么在两种情况下，法律上必然等于弱从属：首先，当下属是确定性的，其次，当它具有有限活性时，它是纯净的。
Consider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of the subordinator are indistinguishable within each stack, then strong subordination produces a Lévy process, otherwise it may not. Weak subordination was introduced to extend strong subordination, always producing a Lévy process even when strong subordination does not. Here, we prove that strong and weak subordination are equal in law under the aforementioned condition. In addition, we prove that if strong subordination is a Lévy process, then it is necessarily equal in law to weak subordination in two cases: firstly, when the subordinator is deterministic and secondly, when it is pure-jump with finite activity.
