Chung's Law and The Csáki Function

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Abstract

We have found the limit

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.

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