Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  711.60025
Autor:  Erdös, Paul; Révész, P.
Title:  A new law of iterated logarithm. (In English)
Source:  Acta Math. Hung. 55, No. ½, 125-131 (1990).
Review:  The authors study the limit behaviour as t ––> oo of the process

\xi(t) = \sup {s:  e \leq s \leq t,  W(s) \geq (2s log log s) ½},

where W(t) is a Wiener process. The main result is the following Theorem:

liminft ––> oo[\frac{log log t) ½}{(log log log t)· log t}] log \frac{\xi (t)}{t} = -C  a.s.,

where C is a positive constant and 2-2 \leq C \leq 214.
Reviewer:  I.S.Borisov
Classif.:  * 60F15 Strong limit theorems
                   60G15 Gaussian processes
                   60J65 Brownian motion
Keywords:  law of iterated logarithm; Wiener process

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