Abstract
Under appropriate assumptions, the martingale approximation method allows us to reduce the study of the asymptotic behavior of sums of random variables that form a stationary random sequence to a similar problem for sums of stationary martingale differences. In an early paper on the martingale method, the author have proposed certain sufficient conditions for the central limit theorem to hold. It is shown in the present note that these conditions, at least in one particular case, can be essentially relaxed. In the context of the central limit theorem for Markov chains, a similar observation was done in a recent Holzmann and author's work. Bibliography: 12 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 124–132.
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Gordin, M.I. A Note on the Martingale Method of Proving the Central Limit Theorem for Stationary Sequences. J Math Sci 133, 1277–1281 (2006). https://doi.org/10.1007/s10958-006-0036-7
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DOI: https://doi.org/10.1007/s10958-006-0036-7