The Annals of Probability

Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm

Alejandro de Acosta

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Abstract

We prove a small deviation theorem of a new form for the functional central limit theorem for partial sums of independent, identically distributed finite-dimensional random vectors. The result is applied to obtain a functional form of the Chung-Jain-Pruitt law of the iterated logarithm which is also a strong speed of convergence theorem refining Strassen's invariance principle.

Article information

Source
Ann. Probab. Volume 11, Number 1 (1983), 78-101.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176993661

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176993661

Mathematical Reviews number (MathSciNet)
MR682802

Zentralblatt MATH identifier
0504.60033

Subjects
Primary: 60F15: Strong theorems

Keywords
Small deviations other law of the iterated logarithm Strassen's invariance principle

Citation

de Acosta, Alejandro. Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm. The Annals of Probability 11 (1983), no. 1, 78--101. doi:10.1214/aop/1176993661. http://projecteuclid.org/euclid.aop/1176993661.


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