On bifractional Brownian motion

Abstract

This paper is devoted to analyzing 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 fractional Brownian motion (which is obtained for K = 1 ). Here, we adopt the strategy of stochastic calculus via regularization. Of particular interest to us is the case H K = 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 standard Brownian motion. It is a short-memory process even though it is neither a semimartingale nor a Dirichlet process.