Deviation probability bounds for fractional martingales and related   remarks
  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. 
Bruno Saussereau
math.PR math.ST stat.TH