A survey of functional laws of the iterated logarithm for self-similar processes
Files
Accepted manuscript
Date
1984-01
DOI
Authors
Taqqu, Murad S.
Czado, Claudia
Version
OA Version
Citation
Murad S Taqqu, Claudia Czado. 1984. "A survey of functional laws of the iterated logarithm for self-similar processes." Communications in Statistics. Stochastic Models, Volume 1, pp. 77 - 115. https://doi.org/10.1080/15326348508807005
Abstract
A process X(t) is self-similar with index H > 0 if the finite-dimensional distributions of X(at) are identical to those of aHX(t) for all a > 0. Consider self-similar processes X(t) that are Gaussian or that can be represented throught Wiener-Itô integrals. The paper surveys functional laws of the iterated logarithm for such processes X(t) and for sequences whose normalized sums coverage weakly to X(t). The goal is to motivate the results by including outline of proofs and by highlighting relationships between the various assumptions.
The paper starts with a general discussion fo functional laws of the iterated logarithm, states some of their formulations and sketches the reproducing kernal Hilbert space set-up.