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Large Favourite Sites of Simple Random Walk and theWiener Process


 
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1. Title Title of document Large Favourite Sites of Simple Random Walk and theWiener Process
 
2. Creator Author's name, affiliation, country Endre Csaki; Hungarian Academy of Sciences
 
2. Creator Author's name, affiliation, country Zhan Shi; Université de Paris VI
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Local time,favourite site, random walk, Wiener process
 
3. Subject Subject classification 60J55; 60J15, 60J65
 
4. Description Abstract Let $U(n)$ denote the most visited point by a simple symmetric random walk $\{ S_k\}_{k\ge 0}$ in the first $n$ steps. It is known that $U(n)$ and $max_{0\le k\le n} S_k$ satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. Lévy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The corresponding problem for the Wiener process is also studied.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1998-09-30
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/36
 
10. Identifier Digital Object Identifier 10.1214/EJP.v3-36
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 3
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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