Mixtures of higher-order fractional Brownian motions

被引：9
|
作者：
El Omari, Mohamed [1 ]
机构：
[1] Fac Sci & Tech, Dept Appl Math, Beni Mellal 23000, Morocco
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2023年 / 52卷 / 12期
关键词：
nth order fractional Brownian motion; self-similarity; long-range dependence; semimatingale property; non Markovian process; OPTIONS;
D O I：
10.1080/03610926.2021.1986541
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this article, we show that the nth-order fractional Brownian motions (fBm) introduced by Perrin et al. are non Markovian special semimartingales. Their infinite mixtures are also presented and shown to be semimartingales satisfying mixed self-similarity property and accounting for long-range dependence phenomena. As result, they are alternative to mixed fBm in modeling stock prices in arbitrage-free financial markets.
引用
收藏
页码：4200 / 4215
页数：16
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