Deviation probability bounds for fractional martingales and related remarks

2012/04/19 by Bruno Saussereau, Saussereau, Bruno
Mathematics · #60B12 #60G22 #60G48 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60B12 #msc:60G22 #msc:60G48 #stat.TH

paper · pdf · doi:10.48550/arxiv.1204.4268

arxiv created 2012/04/19 · arxiv updated 2012/04/20

Abstract

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 β-variation of the fractional martingale. A non trivial example of application of this convergence result is proposed.

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