On the local time process standardized by the local time at zero
Let L(a,t) be the (jointly continuous) local time of a Wiener process. The following iterated logarithm law is proved: For \(a\in R\) and \(\alpha\leq 1/2\) \[ \limsup_{t\to \infty}\frac{| L(a,t)- L(0,t)|}{t^{(1-2\alpha)/4}(L(0,t)\quad)^{\alpha}(\log \log t)^{(3-2\alpha)/4}}=| a|^{1/2}K_{\alpha}\quad a.s. \] with explicitly given \(K_{\alpha}\).
scientific article; zbMATH DE number 4064200