## The Annals of Probability

### Dominating Points and the Asymptotics of Large Deviations for Random Walk on $\mathbb{R}^d$

Peter Ney

#### Abstract

Let $\mu(\cdot)$ be a probability measure on $\mathbb{R}^d$ and $B$ be a convex set with nonempty interior. It is shown that there exists a unique "dominating" point associated with $(\mu, B)$. This fact leads (via conjugate distributions) to a representation formula from which sharp asymptotic estimates of the large deviation probabilities $\mu^{\ast n}(nB)$ can be derived.

#### Article information

Source
Ann. Probab., Volume 11, Number 1 (1983), 158-167.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993665

Digital Object Identifier
doi:10.1214/aop/1176993665

Mathematical Reviews number (MathSciNet)
MR682806

Zentralblatt MATH identifier
0503.60035

JSTOR
Ney, Peter. Dominating Points and the Asymptotics of Large Deviations for Random Walk on $\mathbb{R}^d$. Ann. Probab. 11 (1983), no. 1, 158--167. doi:10.1214/aop/1176993665. https://projecteuclid.org/euclid.aop/1176993665