Some extract rates in the functional law of the iterated logarithm

Philippe Berthet; Mikhail Lifshits

doi:10.1016/S0246-0203(02)01131-7

Some extract rates in the functional law of the iterated logarithm

Philippe Berthet, Mikhail Lifshits

Факультет математико-механический

Research output

6 Citations (Scopus)

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_αx^α with α ∈ ]1/2, 1[, thus solving a small ball estimate problem which was open for ten years.

Original language	English
Pages (from-to)	811-824
Number of pages	14
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	38
Issue number	6
DOIs	https://doi.org/10.1016/S0246-0203(02)01131-7
Publication status	Published - 1 Jan 2002

Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/S0246-0203(02)01131-7

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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 cαxα with α ∈ ]1/2, 1[, thus solving a small ball estimate problem which was open for ten years.",

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