## The Annals of Probability

### Large deviation probabilities and dominating points for open convex sets: nonlogarithmic behavior

J. Kuelbs

#### Abstract

The existence of a dominating point for an open convex set and a corresponding representation formula for large deviation probabilities are established in the infinite-dimensional setting under conditions which are both necessary and sufficient and follow from those used previously in $\mathbb{R}^d$ . A precise nonlogarithmic estimate of large deviation probabilities applicable to Gaussian measures is also included.

#### Article information

Source
Ann. Probab. Volume 28, Number 3 (2000), 1259-1279.

Dates
First available in Project Euclid: 18 April 2002

http://projecteuclid.org/euclid.aop/1019160334

Digital Object Identifier
doi:10.1214/aop/1019160334

Mathematical Reviews number (MathSciNet)
MR1797312

Zentralblatt MATH identifier
1023.60006

#### Citation

Kuelbs, J. Large deviation probabilities and dominating points for open convex sets: nonlogarithmic behavior. Ann. Probab. 28 (2000), no. 3, 1259--1279. doi:10.1214/aop/1019160334. http://projecteuclid.org/euclid.aop/1019160334.

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