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

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Date
2009
Volume
1461
Issue
Journal
Series Titel
WIAS Preprints
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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 König 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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Citation
König, W., & Schmid, P. (2009). Random walks conditioned to stay in Weyl chambers of type C and D. Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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