On the local time process standardized by the local time at zero
type: Item
instance of: scholarly article
title: On the local time process standardized by the local time at zero
zbMATH Open document ID: 0652.60080
DOI: 10.1007/BF01952489
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: 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 \(K_{\alpha}\).
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4064200
zbMATH Keywords: local time
zbMATH Keywords: iterated logarithm law
author: Endre Csáki
author: Antónia Földes
MaRDI profile type: Publication
cites work: The most visited site of Brownian motion and simple random walk
cites work: On the character of convergence to Brownian local time. II
cites work: Q5827353
cites work: Limit theorems for Lévy processes and Poisson point processes and their applications to Brownian excursions
cites work: Q4169502
full work available at URL: https://doi.org/10.1007/bf01952489
OpenAlex ID: W2025723689
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description: scientific article; zbMATH DE number 4064200