Fractional processes conditioned to stay positive

我们研究了分数布朗运动和相关的分数次过程。我们的目标是定义有条件保持正的分数布朗运动。困难来自于我们条件的事件--永远保持正--的概率为零。此外，所考虑的过程本质上是非马尔可夫的。这个新对象推广了“条件保持为正的布朗运动”。对其他分数次过程的扩展也进行了研究；方法来自于过去5-7年来深入研究的持续概率理论。

We study fractional Brownian motion and related fractional processes. The goal is to define fractional Brownian motion conditioned to stay positive.The difficulty comes from the fact that the event we condition on -- staying positive forever -- has probability zero. Additionally, the considered process is intrinsically non-Markovian.This new object generalizes 'Brownian motion conditioned to stay positive'. Extensions to other fractional processes are also investigated; methods come from the theory of persistence probabilities studied intensively over the last 5-7 years.