no. 1
An extension of the standard multifractional Brownian motion
Mohamed Ait Ouahra1 ; Mohamed Mellouk2 ; Hanae Ouahhabi3 ; Aissa Sghir1
1 Mohammed First University. Faculty of Sciences Oujda. Department of Mathematics. Stochastic and Deterministic Modelling Laboratory. B.P. 717. Morocco.
2 MAP5, UMR CNRS 8145, Université Paris Cité, 45 rue des Saints-Pères, 75006 Paris, France
3 Department of Statistics. College of Business and Economics. United Arab Emirates University.
Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 1, pp. 167-184.

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

Publié le :
DOI : 10.5802/ambp.436
Classification : 60G15, 60G17, 60G18, 60G22
Keywords: Gaussian process, Self similar process, Fractional Brownian motion, Bifractional Brownian motion, Multifractional Brownian motion, Local asymptotic self-similarity, Long range dependence

Mohamed Ait Ouahra 1 ; Mohamed Mellouk 2 ; Hanae Ouahhabi 3 ; Aissa Sghir 1

1 Mohammed First University. Faculty of Sciences Oujda. Department of Mathematics. Stochastic and Deterministic Modelling Laboratory. B.P. 717. Morocco.
2 MAP5, UMR CNRS 8145, Université Paris Cité, 45 rue des Saints-Pères, 75006 Paris, France
3 Department of Statistics. College of Business and Economics. United Arab Emirates University.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mohamed Ait Ouahra; Mohamed Mellouk; Hanae Ouahhabi; Aissa Sghir. An extension of the standard multifractional Brownian motion. Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 1, pp. 167-184. doi : 10.5802/ambp.436. https://ambp.centre-mersenne.org/articles/10.5802/ambp.436/

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