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Generalized Wiener–Hermite integrals and rough non-Gaussian Ornstein–Uhlenbeck process
Stochastics ( IF 0.9 ) Pub Date : 2022-04-30 , DOI: 10.1080/17442508.2022.2068955 Obayda Assaad 1 , Charles-Phillipe Diez 1 , Ciprian A. Tudor 1
中文翻译:
广义 Wiener–Hermite 积分和粗糙的非高斯 Ornstein–Uhlenbeck 过程
更新日期:2022-04-30
Stochastics ( IF 0.9 ) Pub Date : 2022-04-30 , DOI: 10.1080/17442508.2022.2068955 Obayda Assaad 1 , Charles-Phillipe Diez 1 , Ciprian A. Tudor 1
Affiliation
We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval . We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.
中文翻译:
广义 Wiener–Hermite 积分和粗糙的非高斯 Ornstein–Uhlenbeck 过程
我们讨论了广义 Hermite 过程的几个性质,它是一个非高斯自相似过程,自相似指数属于整个区间. 我们还针对此过程定义了 Wiener 积分,作为一个应用,我们定义并研究了其相关的 Ornstein-Uhlenbeck 过程。