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Random walks conditioned to stay in Weyl chambers of type C and D


 
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1. Title Title of document Random walks conditioned to stay in Weyl chambers of type C and D
 
2. Creator Author's name, affiliation, country Wolfgang König; Technical University Berlin
 
2. Creator Author's name, affiliation, country Patrick Schmid; Universität Leipzig
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Conditional random walks, Doob $h$-transform, non-colliding probability, harmonic functions, réduite, Weyl chamber
 
3. Subject Subject classification 60G50, 60F17
 
4. Description Abstract We construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob $h$-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an $h$-transform in the Weyl chamber of type C.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) DFG-Graduiertenkolleg "Analysis, Geometrie und ihre Verbindung zu den Naturwissenschaften"
 
7. Date (YYYY-MM-DD) 2010-04-07
 
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/1560
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1560
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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