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Journal Articles Communications on Stochastic Analysis Year : 2011

## An extension of bifractional Brownian motion

(1) , (2)
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Xavier Bardina
• Function : Author
• PersonId : 867299
Khalifa Es-Sebaiy
• Function : Correspondent author
• PersonId : 867300

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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 $2HK=1$.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-00457155 , version 1 (17-02-2010)
hal-00457155 , version 2 (09-05-2011)

### Identifiers

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

### Cite

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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