Prépublication numéro 2005-08 du laboratoire LAGA, Université Paris 13 |

**Résumé:** This paper is devoted to analyze several properties of the
bifractional Brownian motion introduced by Houdré and Villa.
This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of the fractional Brownian motion (which is obtained for K=1).
We adopt the strategy of the stochastic calculus
via regularization. Particular interest has for us the
case HK=1/2. In this case, the process is a finite
quadratic variation process with bracket equal to a
constant times t and it has the same order
of self-similarity as the standard Brownian motion.
It is a short memory process even though it is neither a semimartingale nor a Dirichlet process.

**Code(s) de Classification MSC2000: **60H05 Stochastic integrals
; 60G15 Gaussian processes
; 60G18 Self-similar processes
;

**Mots Clés:** * Bifractional Brownian motion; Dirichlet processes; self-similar processes; calculus via regularization.*

**Langue du texte: ** *Anglais *

**Article reçu:** 2005-03-11