Deviation probability bounds for fractional martingales and related remarks

Details Deviation probability bounds for fractional martingales and related remarks Deviation probability bounds for fractional martingales and related remarks

2012-04-19

arxiv.org/abs/1204.4268v1

Mathematics

Probability

Scientific paper

In this paper we prove exponential inequalities (also called Bernstein's
inequality) for fractional martingales. As an immediate corollary, we will
discuss weak law of large numbers for fractional martingales under divergence
assumption on the $\beta-$variation of the fractional martingale. A non trivial
example of application of this convergence result is proposed.

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