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Representations of hermite processes using local time of intersecting stationary stable regenerative sets
Journal of Applied Probability ( IF 1 ) Pub Date : 2020-11-23 , DOI: 10.1017/jpr.2020.57
Shuyang Bai

Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

中文翻译:

使用相交的静止稳定再生集的本地时间表示 Hermite 过程

Hermite 过程是一类具有固定增量的自相似过程。它们经常出现在长期依赖下的极限定理中。我们推导出具有多个 Wiener-Itô 积分的 Hermite 过程的新表示,其被积函数涉及相交的静止稳定再生集的本地时间。该证明依赖于基于随机区间覆盖方案的再生集和本地时间的近似。
更新日期:2020-11-23
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