Strassen-type functional laws for strong topologies
Let \(W(\cdot)\) denote a Wiener process. The functional law of the iterated logarithm due to \textit{V. Strassen} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 3, 211-226 (1964; Zbl 0132.129)] establishes that the sequence \(\{(2nLLn)^{-1/2}W(ns)\}\) of functions of \(s\in[0,1]\) is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. We obtain a general characterization of the topologies under which this statement remains valid.
scientific article; zbMATH DE number 568984
scientific article