Electronic Resource
Springer
Acta applicandae mathematicae
38 (1995), S. 109-129
ISSN:
1572-9036
Keywords:
60F10
;
60G42
;
Key words
;
Central limit theorem
;
large deviations
;
martingales
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let(X i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence $$P\left\{ {\sum\limits_{k = 1}^n {X_k } 〉 \sqrt n r} \right\}/P\{ Y 〉 r\} \to 0asn \to \infty ,$$ asn → ∞, over 0⩽r⩽o(n1/6) in the case of bounded martingale differences. The results are applied to prove large deviations for the ‘baker transformation’. Moderate deviations for martingales are also discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00992617
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