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An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales

Author

Listed:
  • I. G. Grama

    (Université de Bretagne Sud)

  • E. Haeusler

    (University of Giessen)

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.

Suggested Citation

  • I. G. Grama & E. Haeusler, 2006. "An Asymptotic Expansion for Probabilities of Moderate Deviations for Multivariate Martingales," Journal of Theoretical Probability, Springer, vol. 19(1), pages 1-44, January.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:1:d:10.1007_s10959-006-0001-x
    DOI: 10.1007/s10959-006-0001-x
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    References listed on IDEAS

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    1. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
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    Cited by:

    1. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.

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