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 Electronic Journal of Probability > Vol. 15(2010) > Paper 11 open journal systems 


Conditional limit theorems for ordered random walks

Denis E Denisov, Cardiff University
Vitali Wachtel, University of Munich


Abstract
In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the optimal moment assumptions for the construction proposed by Eichelsbacher and Koenig, and generalise the limit theorem for this conditional process.


Full text: PDF

Pages: 292-322

Published on: April 8, 2010
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Electronic Journal of Probability. ISSN: 1083-6489