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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 371025, 7 pages
http://dx.doi.org/10.1155/2012/371025
Research Article

On Tightness of the Skew Random Walks

Department of Mathematics, Iowa State University, Ames, IA 50010, USA

Received 8 August 2011; Accepted 5 December 2011

Academic Editor: Nikolaos E. Limnios

Copyright © 2012 Youngsoo Seol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The primary purpose of this paper is to prove a tightness of 𝛼 -skew random walks. The tightness result implies, in particular, that the 𝛼 -skew Brownian motion can be constructed as the scaling limit of such random walks. Our proof of tightness is based on a fourth-order moment method.