Transient Nearest Neighbor Random Walk and Bessel Process

Endre Csáki (), Antónia Földes () and Pál Révész ()
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Endre Csáki: Hungarian Academy of Sciences
Antónia Földes: College of Staten Island, CUNY
Pál Révész: Technische Universität Wien

Journal of Theoretical Probability, 2009, vol. 22, issue 4, 992-1009

Abstract: Abstract We prove a strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. We show that their local times are close enough to share the same strong limit theorems. It is also shown that if the difference between the distributions of two NN random walks are small, then the walks themselves can be constructed in such a way that they are close enough. Finally, some consequences concerning strong limit theorems are discussed.

Keywords: Transient random walk; Bessel process; Strong invariance principle; Local time; Strong theorems; 60F17; 60F15; 60J10; 60J55; 60J60 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-008-0165-7

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