Journal of Theoretical Probability

, Volume 1, Issue 2, pp 115-119

First online:

On some results of M. I. Gordin: A clarification of a misunderstanding

  • Richard C. BradleyAffiliated withDepartment of Mathematics, Indiana University

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M. I. Gordin proved a central limit theorem for some strictly stationary strongly mixing random sequences without the assumption of finite second moments. Because of a series of misunderstandings, his own correct formulation of the theorem has been essentially ignored, while an incorrect formulation has been discussed extensively and attributed to him in many references. This note explains in detail what has happened, in the hope of clearing up the misunderstandings.

Key Words

Central limit theorem strong mixing infinite variance Martingale theory