Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic
| dc.creator | Raschel, Kilian | |
| dc.date | 2009-02-16 | |
| dc.date.accessioned | 2026-07-07T12:42:49Z | |
| dc.date.available | 2026-07-07T12:42:49Z | |
| dc.description | Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabilities at a given time and at a given site are made explicit. The following asymptotics for these random walks starting from a given point $(n_0,m_0)$ are computed : that of probabilities of being absorbed at a given site $(i,0)$ [resp. $(0,j)$] as $i\to \infty$ [resp. $j \to \infty$], that of the distribution's tail of absorption time at x-axis [resp. y-axis], that of the Green functions at site $(i,j)$ when $i,j\to \infty$ and $j/i \to \tan γ$ for $γ\in [0, π/2]$. These results give the Martin boundary of the process and in particular the suitable Doob $h$-transform in order to condition the process never to reach the boundary. They also show that this $h$-transformed process is equal in distribution to the limit as $n\to \infty$ of the process conditioned by not being absorbed at time $n$. The main tool used here is complex analysis. | |
| dc.identifier | https://arxiv.org/abs/0902.2785 | |
| dc.identifier | http://arxiv.org/abs/0902.2785 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220210 | |
| dc.subject | Probability | |
| dc.subject | Complex Variables | |
| dc.subject | 60G50, 60G40, 31C35 (Primary) 30E20, 30E25 (Secondary) | |
| dc.title | Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic | |
| dc.type | text |