An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales

I. G. Grama () and E. Haeusler ()
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I. G. Grama: Université de Bretagne Sud
E. Haeusler: University of Giessen

Journal of Theoretical Probability, 2006, vol. 19, issue 1, 1-44

Abstract: 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.

Keywords: Martingales; moderate deviations; rate of convergence (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0001-x

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