On the Central Limit Question Under Absolute Regularity

Davydov showed that in a classic central limit theorem of Ibragimov under the strong mixing condition, the combinations of mixing rate and moment assumption were practically as weak as permissible. Here some constructions will be given to show that Davydov's observation still holds under the additional assumption that the growth of var(X₁ + ⋯ + Xₙ) be asymptotically linear. Our constructions will be similar to a recent one of Herrndorf.