Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes

Are fractional Brownian motions predictable?

We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. Mathematics Subject Classification (2000). Primary 60G07; Secondary 60G15, 60G48, 60G25.

9 Are fractional Brownian motions predictable ?

We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. 1 Intoduction The question in the title is provocative, of course. Everybody familiar with the theory of stochast...

Fuzzy Modelling Stochastic Processes Describing Brownian Motions

Exponents, symmetry groups and classification of operator fractional Brownian motions

Operator fractional Brownian motions (OFBMs) are zero mean, operator self-similar (o.s.s.), Gaussian processes with stationary increments. They generalize univariate fractional Brownian motions to the multivariate context. It is well-known that the so-called symmetry group of an o.s.s. process is conjugate to subgroups of the orthogonal group. Moreover, by a celebrated result of Hudson and Maso...

Type I and type II fractional Brownian motions: A reconsideration

This paper reviews the di¤erences between the so-called type I and type II models of fractional Brownian motion, corresponding to the cases in which pre-sample shocks are either included in the lag structure, or suppressed. It is noted that there can be substantial di¤erences between the distributions of these two processes, and of functionals derived from them, so that it becomes an important ...