Electronic Journal of Probability

Conditional Limit Theorems for Ordered Random Walks

Denis Denisov and Vitali Wachtel

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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.

Article information

Electron. J. Probab. Volume 15 (2010), paper no. 11, 292-322.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60F17: Functional limit theorems; invariance principles

Dyson's Brownian Motion Doob h-transform Weyl chamber

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Denisov, Denis; Wachtel, Vitali. Conditional Limit Theorems for Ordered Random Walks. Electron. J. Probab. 15 (2010), paper no. 11, 292--322. doi:10.1214/EJP.v15-752. https://projecteuclid.org/euclid.ejp/1464819796

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