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An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales

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We derive formulae for probabilities of large deviations in a moderate range for multivariate martingales. Although we give an elementary proof for univariate martingales, there is no elementary extension to the multivariate case. The hard point is to produce a proper estimate for the norming factor. For this we develop a method of sequential projectors which allows us to obtain the desired natural extension of the result in the univariate case.

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Authors and Affiliations

  1. SABRES, Université de Bretagne Sud, Campus Tohannic, Centre de Recherche Yves Coppens, 56017, Vannes, France

    I. G. Grama

  2. Mathematical Institute, University of Giessen, Arndtstr. 2, 35392, Giessen, Germany

    E. Haeusler

Authors
  1. I. G. Grama
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  2. E. Haeusler
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Correspondence to E. Haeusler.

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Grama, I.G., Haeusler, E. An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales. J Theor Probab 19, 1–44 (2006). https://doi.org/10.1007/s10959-006-0001-x

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  • DOI: https://doi.org/10.1007/s10959-006-0001-x

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