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


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.


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Wolfgang König. Patrick Schmid. "Random walks conditioned to stay in Weyl chambers of type C and D." Electron. Commun. Probab. 15 286 - 296, 2010.


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

Primary: 60G50
Secondary: 60F17

Keywords: conditional random walks , Doob $h$-transform , Harmonic functions , non-colliding probability , réduite , Weyl chamber

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