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Capacity Estimates, Boundary Crossings and the Ornstein-Uhlenbeck Process in Wiener Space

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Capacity Estimates, Boundary Crossings and the Ornstein-Uhlenbeck Process in Wiener Space
2.	Creator	Author's name, affiliation, country	Endre Csaki; Hungarian Academy of Sciences
2.	Creator	Author's name, affiliation, country	Davar Khoshnevisan; University of Utah
2.	Creator	Author's name, affiliation, country	Zhan Shi; Université Paris VI
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Capacity on Wiener space, quasi-sure analysis, Ornstein-Uhlenbeck process,Brownian sheet.
3.	Subject	Subject classification	Primary 60G60; Secondary 60J60.
4.	Description	Abstract	Let $T_1$ denote the first passage time to 1 of a standard Brownian motion. It is well known that as $\lambda$ goes to infinity, $P\{ T_1 > \lambda \}$ goes to zero at rate $c \lambda^{-1/2}$, where $c$ equals $(2/ \pi)^{1/2}$. The goal of this note is to establish a quantitative, infinite dimensional version of this result. Namely, we will prove the existence of positive and finite constants $K_1$ and $K_2$, such that for all $\lambda>e^e$, $$K_1 \lambda^{-1/2} \leq \text{Cap} \{ T_1 > \lambda\} \leq K_2 \lambda^{-1/2} \log^3(\lambda) \cdot \log\log(\lambda),$$ where `$\log$' denotes the natural logarithm, and $\text{Cap}$ is the Fukushima-Malliavin capacity on the space of continuous functions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-11-20
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1011
10.	Identifier	Digital Object Identifier	10.1214/ECP.v4-1011
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 4
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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