An intermediate Baum-Katz theorem

Allan Gut (1) , Ulrich Stadtmüller (2)

1 Department of Mathematics [Uppsala]
2 Department of Number Theory and Probability Theory

We extend the classical Hsu-Robbins-Erdős theorem to the case when all moments exist, but the moment generating function does not, viz., we assume that for some . We also present multiindex versions of the same and of a related result due to Lanzinger in which the assumption is that for some .

Mots clés: primary; secondary; Sums of i.i.d. random variables; Convergence rates; Law of large numbers; Almost exponential moments; Random fields; Multiindex

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Allan Gut, Ulrich Stadtmüller. An intermediate Baum-Katz theorem. Statistics and Probability Letters, 2011, 81 (10), pp.1486. ⟨10.1016/j.spl.2011.05.008⟩. ⟨hal-00770344⟩