Geodesic
Semi-additive functionals and cocycles in the context of self-similarity
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 149-177

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Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.
Keywords: stable, self-similar processes with stationary increments, mixed moving averages, nonsingular flows, cocycles, semi-additive functionals 
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Pipiras, Vladas; Taqqu, Murad. Semi-additive functionals and cocycles in the context of self-similarity. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 149-177. http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a0/