论文标题
通过曲线爬行莱维过程
Creeping of Lévy processes through curves
论文作者
论文摘要
据说，如果在此曲线的第一个通道时，则据说levy过程会逐渐蔓延。我们首先研究了双变量下属的该属性。给定图形$ \ {（t，f（t））：t \ ge0 \} $的任何连续，非增加功能$ f $的$ f $，以使$ f（0）> 0 $，我们表达了一种概率，即双向下in子源$（y，z）$的可能性通过此图形从0 creeps发出的groce and renewal $ y n renewal $ y zon $ y n renewal $ y n renewal $ y n renewal $ y，我们将此结果应用于任何真实的lévy过程的爬行概率，该图在该过程也达到其过去的至上的时间时，任何连续的，非增加功能的图表。这种概率涉及双变量向上梯子过程的更新功能的密度以及其漂移系数。我们还调查了Lévy过程的情况，以在函数图下方的最后一个通道时间保持正向蔓延。然后，我们提供了一些示例，并将其应用于稳定的Ornstein-Uhlenbeck过程中在固定水平上爬行的可能性。我们还沿着文本提出了几个公开问题。
A Lévy process is said to creep through a curve if, at its first passage time across this curve, the process reaches it with positive probability. We first study this property for bivariate subordinators. Given the graph $\{(t,f(t)):t\ge0\}$ of any continuous, non increasing function $f$ such that $f(0)>0$, we give an expression of the probability that a bivariate subordinator $(Y,Z)$ issued from 0 creeps through this graph in terms of its renewal function and the drifts of the components $Y$ and $Z$. We apply this result to the creeping probability of any real Lévy process through the graph of any continuous, non increasing function at a time where the process also reaches its past supremum. This probability involves the density of the renewal function of the bivariate upward ladder process as well as its drift coefficients. We also investigate the case of Lévy processes conditioned to stay positive creeping at their last passage time below the graph of a function. Then we provide some examples and we give an application to the probability of creeping through fixed levels by stable Ornstein-Uhlenbeck processes. We also raise a couple of open questions along the text.
