Conditional limit theorems for ordered random walks

Denisov, Denis and Wachtel, V. 2010. Conditional limit theorems for ordered random walks. Electronic Journal of Probability 15 , pp. 292-322.

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Abstract

In a recent paper of Eichelsbacher and K�onig (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 �nd the optimal moment assumptions for the construction proposed by Eichelsbacher and K�onig, and generalise the limit theorem for this conditional process.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Dyson's Brownian Motion, Doob h-transform, Weyl chamber
Publisher:	Institute of Mathematical Statistics
ISSN:	1083-6489
Last Modified:	26 Jun 2019 01:56
URI:	https://orca.cardiff.ac.uk/id/eprint/11066

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