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 Electronic Communications in Probability > Vol. 15(2010) > Paper 27 open journal systems 


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

Wolfgang König, Technical University Berlin
Patrick Schmid, Universität Leipzig


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.


Full text: PDF

Pages: 286-296

Published on: July 23, 2010
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Electronic Communications in Probability. ISSN: 1083-589X