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

被引：0
作者：
Alain Rouault
Marc Yor
Marguerite Zani
机构：
[1] LAMA,Laboratoire de Probabilités
[2] Université de Versailles,undefined
[3] Université Paris 6,undefined
[4] Site Chevaleret,undefined
[5] Université des Sciences et Technologies de Lille U.F.R. de Mathématiques,undefined
[6] Bât,undefined
来源：
Journal of Theoretical Probability | 2002年 / 15卷
关键词：
Arc-sine law; large deviations; Ornstein–Uhlenbeck process;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：793 / 815
页数：22
相关论文
共 34 条
[1]  
Breiman L.(1967)First exit times from a square root boundary Fifth Berkeley Symposium 2 9-16
[2]  
Brosamler G. A.(1988)An almost everywhere central limit theorem Math. Proc. Cambridge Philos. Soc. 104 561-574
[3]  
Bryc W.(1996)Large deviations and strong mixing Ann. Inst. H. Poincaré Probab. Statist. 32 549-569
[4]  
Dembo A.(1988)The large deviation principle for hypermixing processes Probab. Theory Related Fields 78 627-649
[5]  
Chiyonobu T.(1992)Invariance principle for logarithmic averages Math.Proc. Cambridge Philos. Soc. 112 195-205
[6]  
Kusuoka S.(1975)Asymptotic evaluation of certain Markov processes for large time, I Comm. Pure Appl. Math. 28 1-47
[7]  
Csorgo M.(1975)Asymptotic evaluation of certain Markov processes for large time, II Comm. Pure Appl. Math. 28 279-301
[8]  
Horvath L.(1976)Asymptotic evaluation of certain Markov processes for large time, III Comm. Pure Appl. Math. 29 389-461
[9]  
Donsker M. D.(1983)Asymptotic evaluation of certain Markov processes for large time, IV Comm. Pure Appl. Math. 36 183-212
[10]  
Varadhan S. R. S.(1953)Changes of signs of sums of random variables Pacific J. Math. 3 673-687
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