The Moduli of Continuity for Operator Fractional Brownian Motion

Abstract

The almost-sure sample path behavior of the operator fractional Brownian motion with exponent D, including multivariate fractional Brownian motion, is investigated. In particular, the global and the local moduli of continuity of the sample paths are established. These results show that the global and the local moduli of continuity of the sample paths are completely determined by the real parts of the eigenvalues of the exponent D, as well as the covariance matrix at some unit vector. These results are applicable to multivariate fractional Brownian motion.