On Ibragimov–Iosifescu conjecture for φ-mixing sequences

doi:10.1016/0304-4149(90)90008-G

Stochastic Processes and their Applications

Volume 35, Issue 2, August 1990, Pages 293-308

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Abstract

The aim of this paper is to give new central limit theorems and invariance principles for φ-mixing sequences of random variables that support the Ibragimov–Iosifescu conjecture. A related conjecture is formulated and a positive answer is given for the distributions that have tails regularly varying with the exponent –2.

MSC

Primary 60F05

60B10

Keywords

φ-mixing sequences

central limit theorem

invariance principle