Translator Disclaimer
2010 Random walks conditioned to stay in Weyl chambers of type C and D
Wolfgang König, Patrick Schmid
Author Affiliations +
Electron. Commun. Probab. 15: 286-296 (2010). DOI: 10.1214/ECP.v15-1560

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.

Citation

Download Citation

Wolfgang König. Patrick Schmid. "Random walks conditioned to stay in Weyl chambers of type C and D." Electron. Commun. Probab. 15 286 - 296, 2010. https://doi.org/10.1214/ECP.v15-1560

Information

Accepted: 7 April 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60067
MathSciNet: MR2670195
Digital Object Identifier: 10.1214/ECP.v15-1560

Subjects:
Primary: 60G50
Secondary: 60F17

JOURNAL ARTICLE
11 PAGES


SHARE
Back to Top