ADDENDUM to:

A Characterization of m-dependent Stationary Infinitely Divisible Sequences with Applications to Weak Convergence (with D. Harrelson). Annals of Probability 2003.

As noticed by Mayer-Wolf, Roitershtein and Zeitouni, our citing of Theorem 1.1 (attributed to Jakubowski and Kobus) is incorrect, since it has not been proved under the conditions given. The reader is thus referred to Theorem 5.3 in Jakubowski and Kobus (1989) for a proof of Theorem 1.1 under slightly stronger conditions. This does not affect any of the results of our paper.

On an unrelated matter, we should have cited the seminal paper of Hoeffding and Robbins (1948) where a CLT for m-dependent random variables is proved. We were unaware of it.

References

• Hoeffding, W. and Robbins, H. (1948) The Central Limit Theorem for Dependent Random Variables. Duke Math. J. 15, 773-780.
• Jakubowsli, A. and Kobus, M. (1989) alpha-stable limit theorems for sums of dependent random variables. J. Multivariate Anal. 52, 199-244.