On the $n$th-Order subfractional Brownian motion

Authors : El Omari Mohamed, Mabdaoui Mohamed

Pages : 1396-1407

View : 118 | Download : 389

Publication Date : 2023-10-31

Article Type : Research Paper

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