Abstract
A discussion of the evolution of a notion of strong mixing as a measure of short range dependence and with additional restrictions a sufficient condition for a central limit theorem, is given. A characterization of strong mixing for stationary Gaussian sequences is noted. Examples of long range dependence leading to limit theorems with nonnormal limiting distributions are specified. Open questions concerning limit theorems for finite Fourier transforms are remarked on. There are also related queries on the use of Fourier methods for a class of nonstationary sequences.
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I thank Professor Rafal Kulik for his help in putting this paper into coherent form.
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Rosenblatt, M. (2015). Short Range and Long Range Dependence. In: Dawson, D., Kulik, R., Ould Haye, M., Szyszkowicz, B., Zhao, Y. (eds) Asymptotic Laws and Methods in Stochastics. Fields Institute Communications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3076-0_15
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