- Hacettepe Journal of Mathematics and Statistics
- Cilt: 52 Sayı: 5
- On the $n$th-Order subfractional Brownian motion
On the $n$th-Order subfractional Brownian motion
Authors : El Omari Mohamed, Mabdaoui Mohamed
Pages : 1396-1407
View : 95 | Download : 377
Publication Date : 2023-10-31
Article Type : Research
Abstract :In the present work, we introduce the $n$th-Order subfractional Brownian motion $S_H^n = \\lbrace S_H^n(t),~t\\geq 0\\rbrace$ with Hurst index $H\\in (n-1,n)$ and order $n\\geq 1$; then we examine some of its basic properties: self-similarity, long-range dependence, non Markovian nature and semimartingale property. A local law of iterated logarithm for $S_H^n$ is also established.Keywords : Gaussian self-similar process, non Markovian process, subfractional Brownian motion, semimartingale property, local law of the iterated logarithm