Fractional integrals of stationary processes and the central limit theorem
- 1 December 1976
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 13 (4) , 723-732
- https://doi.org/10.2307/3212527
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.Keywords
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