Deviation probability bounds for fractional martingales and related remarks
AbstractIn 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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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 8 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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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