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# An extension of bifractional Brownian motion

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Abstract : In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion $B^{H,K}$ with parameters $H\in~(0,1)$ and $K\in(1,2)$ such that $HK\in(0,1)$. A remarkable difference between the case $K\in(0,1)$ and our situation is that this process is a semimartingale when $2HK=1$.
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Document type :
Journal articles
Domain :

https://hal-paris1.archives-ouvertes.fr/hal-00457155
Contributor : Khalifa Es-Sebaiy Connect in order to contact the contributor
Submitted on : Monday, May 9, 2011 - 12:13:30 PM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM
Long-term archiving on: : Wednesday, August 10, 2011 - 2:43:58 AM

### Files

Bardina-Es-Sebaiy.pdf
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### Identifiers

• HAL Id : hal-00457155, version 2
• ARXIV : 1002.3680

### Citation

Xavier Bardina, Khalifa Es-Sebaiy. An extension of bifractional Brownian motion. Communications on Stochastic Analysis, 2011, 5 (2), pp.333-340. ⟨hal-00457155v2⟩

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