Quadratic variations of spherical fractional Brownian motions

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...

Linear-quadratic Control for Stochastic Equations in a Hilbert Space with Fractional Brownian Motions

Convergence of finite-dimensional laws of the weighted quadratic variations process for some fractional Brownian sheets

In this paper we state and prove a central limit theorem for the finite-dimensional laws of the quadratic variations process of certain fractional Brownian sheets. The main tool of this article is a method developed by Nourdin and Nualart in [17] based on the Malliavin calculus.

Asymptotic Behavior of Weighted Quadratic and Cubic Variations of Fractional Brownian Motion

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H . In the quadratic (resp. cubic) case, when H < 1/4 (resp. H < 1/6), we show by means of Malliavin calculus that the convergence holds in L toward an explicit limit which only depends on B. This result is somewhat surprisi...