Csáki, Endre and Földes, Antónia (2022) On the Local Time of the Half-Plane Half-Comb Walk. JOURNAL OF THEORETICAL PROBABILITY, 35. pp. 1247-1261. ISSN 0894-9840
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Official URL: https://doi.org/10.1007/s10959-020-01065-2
Abstract
The Half-Plane Half-Comb walk is a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., horizontal lines below the x-axis are removed. We prove that the probability that this walk returns to the origin in 2N steps is asymptotically equal to 2 / (πN). As a consequence, we prove strong laws and a limit distribution for the local time. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
| Item Type: | Article |
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| Additional Information: | Export Date: 1 February 2021 Correspondence Address: Földes, A.; Department of Mathematics, 2800 Victory Blvd, United States; email: Antonia.Foldes@csi.cuny.edu |
| Uncontrolled Keywords: | Wiener process; Local time; Laws of the iterated logarithm; strong approximation; Anisotropic random walk; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 16 Mar 2023 15:45 |
| Last Modified: | 06 Apr 2023 14:32 |
| URI: | http://real.mtak.hu/id/eprint/162283 |
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