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2010 Conditional Limit Theorems for Ordered Random Walks
Denis Denisov, Vitali Wachtel
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Electron. J. Probab. 15: 292-322 (2010). DOI: 10.1214/EJP.v15-752

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.

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Denis Denisov. Vitali Wachtel. "Conditional Limit Theorems for Ordered Random Walks." Electron. J. Probab. 15 292 - 322, 2010. https://doi.org/10.1214/EJP.v15-752

Information

Accepted: 8 April 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1201.60040
MathSciNet: MR2609589
Digital Object Identifier: 10.1214/EJP.v15-752

Subjects:
Primary: 60G50
Secondary: 60F17, 60G40

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