Are fractional Brownian motions predictable?

Details Are fractional Brownian motions predictable? Are fractional Brownian motions predictable?

2009-07-09

arxiv.org/abs/0907.1618v1

Mathematics

Probability

7 pages, to appear in proceedings of the Sixth Seminar on Stochastic Analysis, Random Fields and Applications, Ascona 2008

Scientific paper

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. The local predictor
of a martingale (in particular: Brownian motion) trivially exists and equals 0.

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