Random Walks on Comb-Type Subsets of $$\mathbb {Z}^2$$ Z 2

Endre Csáki () and Antónia Földes ()
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Endre Csáki: Hungarian Academy of Sciences
Antónia Földes: CUNY

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 2233-2257

Abstract: Abstract We study the path behavior of the simple symmetric walk on some comb-type subsets of $${{\mathbb {Z}}}^2$$ Z 2 which are obtained from $${{\mathbb {Z}}}^2$$ Z 2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.

Keywords: Random walk; 2-dimensional comb; Strong approximation; 2-dimensional Wiener process; Oscillating Brownian motion; Laws of the iterated logarithm; Iterated Brownian motion; Primary 60F17; 60G50; 60J65; Secondary 60F15; 60J10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00938-5

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