Chung's Law and The Csáki Function

Natalia Gorn and Mikhail Lifshits
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Natalia Gorn: Fak. für Mathematik und Informatik

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 399-420

Abstract: Abstract We have found the limit $$L_h = \mathop {\lim \inf }\limits_{T \to \infty } (\log _2 T)^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \left\| {\frac{{W(T \cdot )}}{{(2T\log _2 T)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }} - h} \right\|$$ for a Wiener process W and a class of twice weakly differentiable functions h∈C[0, 1], thus solving the problem of the convergence rate in Chung's functional law for the so-called “slowest points”. Our description is closely related to an interesting functional emerging from a large deviation problem for the Wiener process in a strip.

Keywords: Large deviation; Wiener process (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021678111442

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