## The Annals of Probability

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

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

#### 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

**Digital Object Identifier**

doi:10.1214/aop/1176993661

**Mathematical Reviews number (MathSciNet)**

MR682802

**Zentralblatt MATH identifier**

0504.60033

**JSTOR**

links.jstor.org

**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. Ann. Probab. 11 (1983), no. 1, 78--101. doi:10.1214/aop/1176993661. http://projecteuclid.org/euclid.aop/1176993661.