On a directionally reinforced random walk

Ghosh, Arka; Rastegar, Reza; Roitershtein, Alexander

doi:10.1090/S0002-9939-2014-12030-2

On a directionally reinforced random walk
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by Arka P. Ghosh, Reza Rastegar and Alexander Roitershtein

Proc. Amer. Math. Soc. 142 (2014), 3269-3283

DOI: https://doi.org/10.1090/S0002-9939-2014-12030-2

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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