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Pré-Publication, Document De Travail Année : 2020

An extension of the standard multifractional Brownian motion

M. Ait Ouahra
  • Fonction : Auteur
H. Ouahhabi
  • Fonction : Auteur
A. Sghir
  • Fonction : Auteur
Mohamed Mellouk
  • Fonction : Auteur
  • PersonId : 926222

Résumé

In this paper, firstly, we generalize the definition of the bifractional Brownian motion $B^{H,K}:=\Big(B^{H,K}\;;\;t\geq 0\Big)$, with parameters $H\in(0,1)$ and $K\in(0,1]$, to the case where $H$ is no longer a constant, but a function $H(.)$ of the time index $t$ of the process. We denote this new process by $B^{H(.),K}$. Secondly, we study its time regularities, the local asymptotic self-similarity and the long-range dependence properties. {\bf Key words:} {Gaussian process; Self similar process; Fractional Brownian motion; Bifractional Brownian motion; Multifractional Brownian motion; Local asymptotic self-similarity.}

Dates et versions

hal-04044065 , version 1 (24-03-2023)

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Citer

M. Ait Ouahra, H. Ouahhabi, A. Sghir, Mohamed Mellouk. An extension of the standard multifractional Brownian motion. 2023. ⟨hal-04044065⟩
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