广义Hermite过程(gHp)的Wiener积分。应用范围:具有高频噪声的SDEs

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI:10.1515/rose-2023-2001

Atef Lechiheb

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引用次数: 0

摘要

摘要本文引入广义Hermite过程的Wiener积分，并证明了一个以该积分为极限的非中心极限定理。作为应用，我们研究了以广义Hermite过程作为驱动噪声的相应随机微分方程，证明了解的存在唯一性，并给出了Hermite Ornstein-Uhlenbeck过程和Hermite驱动Vasicek过程的推广。

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Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise

Abstract In this paper, we introduce Wiener integrals with respect to the generalized Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an application, we investigate the corresponding stochastic differential equations with the generalized Hermite process as a driving noise, we prove the existence and the uniqueness of the solution, and we give a generalization of the Hermite Ornstein–Uhlenbeck process and the Hermite-driving Vasicek process.

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量