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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a directionally reinforced random walk


Authors: Arka P. Ghosh, Reza Rastegar and Alexander Roitershtein
Journal: Proc. Amer. Math. Soc. 142 (2014), 3269-3283
MSC (2010): Primary 60F05, 60F15; Secondary 60J25, 70B05
Published electronically: May 19, 2014
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Abstract: We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizsäcker. Our main result is a stable limit theorem for the position of the random walk in higher dimensions. This extends a result of Horváth and Shao that was previously obtained in dimension one only (however, in a more stringent functional form).


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Additional Information

Arka P. Ghosh
Affiliation: Department of Statistics, Iowa State University, Ames, Iowa 50011
Email: apghosh@iastate.edu

Reza Rastegar
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: reza.rastegar80@gmail.com

Alexander Roitershtein
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: roiterst@iastate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12030-2
PII: S 0002-9939(2014)12030-2
Received by editor(s): May 31, 2012
Received by editor(s) in revised form: September 19, 2012
Published electronically: May 19, 2014
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.