Open Access
February, 1978 A Curious Converse of Siever's Theorem
James Lynch
Ann. Probab. 6(1): 169-173 (February, 1978). DOI: 10.1214/aop/1176995623


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.


Download Citation

James Lynch. "A Curious Converse of Siever's Theorem." Ann. Probab. 6 (1) 169 - 173, February, 1978.


Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0378.60016
MathSciNet: MR461630
Digital Object Identifier: 10.1214/aop/1176995623

Primary: 60F10
Secondary: 62E10 , 62E20

Keywords: Large deviation rate

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
Back to Top