文章基本信息

标题：Random walks conditioned to stay in Weyl chambers of type C and D
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作者：König, Wolfgang ; Schmid, Patrick
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2010
卷号：15
页码：286-296
DOI：10.1214/ECP.v15-1560
出版社：Electronic Communications in Probability
摘要：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.
关键词：Conditional random walks, Doob $h$-transform, non-colliding probability, harmonic functions, réduite, Weyl chamber;60G50, 60F17