## The Annals of Mathematical Statistics

### Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws

Thomas A. Hern

#### Abstract

Let $F_n$ denote the distribution function of the $n$th row sum of a triangular array of infinitesimal, rowwise independent random variables, and let $F^\ast$ denote the limiting infinitely divisible distribution function. Bounds are obtained for $\sup_{-\infty < x < \infty} |F_n(x) - F^\ast(x)|$ in the case that the means are finite and also for the attraction to a stable law with exponent $\alpha \leqq 1$. Conditions for convergence of these bounds are given.

#### Article information

Source
Ann. Math. Statist., Volume 43, Number 5 (1972), 1592-1602.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177692391

Digital Object Identifier
doi:10.1214/aoms/1177692391

Mathematical Reviews number (MathSciNet)
MR343346

Zentralblatt MATH identifier
0249.60011

JSTOR

#### Citation

Hern, Thomas A. Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws. Ann. Math. Statist. 43 (1972), no. 5, 1592--1602. doi:10.1214/aoms/1177692391. https://projecteuclid.org/euclid.aoms/1177692391