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Strong Limit Theorems for a Simple Random Walk on the 2-Dimensional Comb


 
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1. Title Title of document Strong Limit Theorems for a Simple Random Walk on the 2-Dimensional Comb
 
2. Creator Author's name, affiliation, country Endre Csáki; Rényi Institute; Hungary
 
2. Creator Author's name, affiliation, country Miklós Csörgö; Carleton University Ottawa; Canada
 
2. Creator Author's name, affiliation, country Antonia Feldes; College of Staten Island New York; United States
 
2. Creator Author's name, affiliation, country Pál Révész; Technical University Vienna; Austria
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walk; 2-dimensional comb; strong approximation; 2-dimensional Wiener process; iterated Brownian motion; Laws of the iterated logarithm
 
3. Subject Subject classification 60F17; 60G50; 60J65; 60J10; 60F15
 
4. Description Abstract We study the path behaviour of a simple random walk on the $2$-dimensional comb lattice $C^2$ that is obtained from $\mathbb{Z}^2$ by removing all horizontal edges off the $x$-axis. In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of the iterated logarithm of its two components, as well as their marginal Hirsch type behaviour.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Hungarian National Foundation for Scientific Research; NSERC Canada; PSC CUNY
 
7. Date (YYYY-MM-DD) 2009-11-01
 
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/710
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-710
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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