Random walks with drift in the positive quadrant
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912887522459648 |
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| author | Nguyen, Tuan Anh Wachtel, Vitali |
| author_facet | Nguyen, Tuan Anh Wachtel, Vitali |
| contents | We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive harmonic functions for such walks and find tail asymptotics for the exit time from the positive quadrant. Moreover, we prove integral and local limit theorems. Finally, we apply our local limit theorems to singular lattice walks with steps $\{(1,-1),(1,1),(-1,1)\}$ and determine asymptotics for the number of walks of length $n$ which end on the line $\{(k,1),\ k\ge1\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random walks with drift in the positive quadrant Nguyen, Tuan Anh Wachtel, Vitali Probability 60G50 We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive harmonic functions for such walks and find tail asymptotics for the exit time from the positive quadrant. Moreover, we prove integral and local limit theorems. Finally, we apply our local limit theorems to singular lattice walks with steps $\{(1,-1),(1,1),(-1,1)\}$ and determine asymptotics for the number of walks of length $n$ which end on the line $\{(k,1),\ k\ge1\}$. |
| title | Random walks with drift in the positive quadrant |
| topic | Probability 60G50 |
| url | https://arxiv.org/abs/2602.07538 |