On the nth-order subfractional Brownian motion

Abstract

In the present work, we introduce the nth-Order subfractional Brownian motion (S_H^n (t), t ≥ 0) with Hurst index H ∈ (n − 1,n) and order n ≥ 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 (t) is also established.