## The Annals of Probability

### A Curious Converse of Siever's Theorem

James Lynch

#### Abstract

A sufficient condition for a sequence of random variables, $T_1, T_2,\cdots$, with cumulant generating functions, $\psi_1, \psi_2,\cdots$, to have a large deviation rate is that $n^{-1}\psi_n(\lambda)\rightarrow \psi(\lambda)$, where $\psi(\lambda)$ satisfies certain regularity conditions. Here it is shown that, when the large deviation rate exists and $T_1, T_2,\cdots$ are properly truncated, it is a necessary condition.

#### Article information

Source
Ann. Probab., Volume 6, Number 1 (1978), 169-173.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995623

Digital Object Identifier
doi:10.1214/aop/1176995623

Mathematical Reviews number (MathSciNet)
MR461630

Zentralblatt MATH identifier
0378.60016

JSTOR