Fractional processes conditioned to stay positive

分数过程有条件保持正值

• 批准号: 403468074
• 负责人: Professor Dr. Frank Aurzada
• 金额: --
• 依托单位: Arbeitsgruppe Stochastik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/403468074?language=en
• 关键词: Fractional; processes; conditioned; stay; positive

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.

研究了分数布朗运动及其相关的分数过程。我们的目标是定义分数布朗运动的条件保持积极的。困难来自于这样一个事实，即我们的条件事件-保持积极的永远-有概率为零。此外，所考虑的过程本质上是非马尔可夫的，这个新的目标推广了“布朗运动条件保持为正”。其他分数过程的扩展也进行了研究，方法来自持久性概率理论，在过去的5-7年里深入研究。