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Some exact rates in the functional law of the iterated logarithm. (English) Zbl 1018.60030
Authors’ abstract: We find exact convergence rate in the Strassen’s functional law of the iterated logarithm for a class of elements on the boundary of the limit set. Our result applies, in particular, to the power functions \(c_\alpha x^\alpha\) with \(\alpha\in ]1/2, 1[\), thus solving a small ball estimate problem which was open for ten years.

MSC:
60F15 Strong limit theorems
60G15 Gaussian processes
60F17 Functional limit theorems; invariance principles
60G12 General second-order stochastic processes
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