A Survey of Functional Laws of the Iterated Logarithm for Self-Similar Processes

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-Ito 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.

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