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Some exact rates in the functional law of the iterated logarithm |
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| Authors: | Philippe Berthet Mikhail Lifshits |
| Affiliation: | a IRMAR, Université Rennes 1, campus de Beaulieu, 35042, Rennes, France;b St-Petersburg State University 198904, Stary Peterhof, Bibliotechnaya pl., 2, Department of Mathematics and Mechanics, Russia;c Université Lille I, 59655, Villeneuve d'Ascq cedex, France |
| 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. |
| Keywords: | Brownian Motion Strassen's and Chung's functional laws Small ball probabilitiesMouvement Brownien Lois fonctionnelles de Strassen et Chung Probabilité s de petite boule |
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