On the $n$th-Order subfractional Brownian motion

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

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