An asymptotic expansion for probabilities of moderate deviations for multivariate martingales

被引：19

作者：

Grama, I. G.

Haeusler, E.

机构：

[1] Univ Giessen, Math Inst, D-35392 Giessen, Germany

[2] Univ Bretagne Sud, SABRES, Ctr Rech Yves Coppens, F-56017 Vannes, France

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2006年 / 19卷 / 01期

关键词：

martingales; moderate deviations; rate of convergence;

D O I：

10.1007/s10959-006-0001-x

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：1 / 44

页数：44

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