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Deviation probability bounds for fractional martingales and related remarks

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  • Saussereau, Bruno

Abstract

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

Suggested Citation

  • Saussereau, Bruno, 2012. "Deviation probability bounds for fractional martingales and related remarks," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1610-1618.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1610-1618
    DOI: 10.1016/j.spl.2012.05.005
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    References listed on IDEAS

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    1. Liptser, R. & Spokoiny, V., 2000. "Deviation probability bound for martingales with applications to statistical estimation," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 347-357, February.
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