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Deviation probability bounds for fractional martingales and related remarks

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  • Saussereau, Bruno
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212001708
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 8 ()
    Pages: 1610-1618

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1610-1618

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    Related research

    Keywords: Fractional martingales; Exponential inequality; Law of large numbers;

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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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