A Large Deviations Principle Related to the Strong Arc-Sine Law

We show a large deviations principle for the family of random variables \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\{ \frac{1}{t}\int_0^t 1 _{B_u } >0du\} $$ \end{document} when t→+∞, where B=(Bu,u≥0) is a standard linear Brownian motion.