A new fluctuation identity for Levy processes and some applications
A new fluctuation identity for Levy processes and some applications
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DOI：
10.2307/3318502
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发表时间：
2001-06-01
期刊：
影响因子：
1.5
通讯作者：
Chaumont, L
中科院分区：
文献类型：
--
作者：
Alili, L;Chaumont, L
设τ和H分别是与给定Levy过程X相关联的梯时和梯高过程。我们给出了（τ，H）与（X，H*）之间的一个恒等式，其中H* 是过程H的右连续逆.这使我们能够获得X的入口定律与反射过程的偏离0的偏移测量的入口定律之间的关系（X-t - inf（s小于或等于t）X（s），t大于或等于0）。在稳定的情况下，提供了一些明确的计算。这些结果也导致了一个明确的形式的入口法律的Levy过程的条件保持积极的。
Let tau and H be respectively the ladder time and ladder height processes associated with a given Levy process X. We give an identity in law between (tau, H) and (X, H*), H* being the right-continuous inverse of the process H. This allows us to obtain a relationship between the entrance law of X and the entrance law of the excursion measure away from 0 of the reflected process (X-t - inf(s less than or equal tot)X(s), t greater than or equal to 0). In the stable case, some explicit calculations are provided. These results also lead to an explicit form of the entrance law of the Levy process conditioned to stay positive.