|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