On the $n$th-Order subfractional Brownian motion

Yıl 2023, Cilt: 52 Sayı: 5, 1396 - 1407, 31.10.2023

El Omari Mohamed Mabdaoui Mohamed

Öz

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.

Anahtar Kelimeler

Gaussian self-similar process, non Markovian process, subfractional Brownian motion, semimartingale property, local law of the iterated logarithm

Kaynakça

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