2006): On the bifractional Brownian motion

This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdre ́ and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes 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 = 12. 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