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The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues


 
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1. Title Title of document The Green Functions of Two Dimensional Random Walks Killed on a Line and their Higher Dimensional Analogues
 
2. Creator Author's name, affiliation, country Kohei Uchiyama; Tokyo Institute of Technology; Japan
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) asymptotic formula, Green function, random walk of zero mean and finite variances, absorption on a line
 
3. Subject Subject classification 60G50
 
4. Description Abstract We obtain asymptotic estimates of the Green functions of random walks on the two-dimensional integer lattice that are killed on the horizontal axis. A basic asymptotic formula whose leading term is virtually the same as the explicit formula for the corresponding Green function of Brownian motion is established under the existence of second moments only. Some refinement of it is given under a slightly stronger moment condition. The extension of the results to random walks on the higher dimensional lattice is also given.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2010-05-19
 
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/793
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-793
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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