Abstract
A class of limit theorems involving asymptotic normality is derived for stationary processes whose spectral density has a singular behavior near frequency zero. Generally these processes have ’long-range dependence’ but are generated from strongly mixing processes by a fractional integral or derivative transformation. Some related remarks are made about random solutions of the Burgers equation.
Received 2 February 1976.
Research carried out while the author was visiting the Australian National University and supported in part by the Office of Naval Research.
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Davis, R.A., Lii, KS., Politis, D.N. (2011). Fractional Integrals of Stationary Processes and the Central Limit Theorem. In: Davis, R., Lii, KS., Politis, D. (eds) Selected Works of Murray Rosenblatt. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8339-8_29
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DOI: https://doi.org/10.1007/978-1-4419-8339-8_29
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