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

2009/11/03 by Wolfgang Koenig, Wolfgang Köenig, Koenig, Wolfgang +2 · 3 citations
Mathematics · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60F17 #msc:60G50

paper · pdf · doi:10.48550/arxiv.0911.0631

12 pages, submitted to ECP

arxiv created 2009/11/03 · arxiv updated 2009/12/01

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.

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• Random walks in Weyl chambers
• First-passage times for random walks with non-identically distributed\n increments
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