On some generalization of fractional Brownian motions

The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Üstünel [Decreusefond L, Üstünel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given.