Electronic Journal of Probability

Conditional Limit Theorems for Ordered Random Walks

Denis Denisov and Vitali Wachtel

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819796

Digital Object Identifier
doi:10.1214/EJP.v15-752

Mathematical Reviews number (MathSciNet)
MR2609589

Zentralblatt MATH identifier
1201.60040

Subjects
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

Keywords
Dyson's Brownian Motion Doob h-transform Weyl chamber

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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