Line crossing problem for biased monotonic random walks in the plane
| dc.creator | Javaheri, Mohammad | |
| dc.date | 2007-09-20 | |
| dc.date.accessioned | 2026-07-07T08:31:21Z | |
| dc.date.available | 2026-07-07T08:31:21Z | |
| dc.description | In this paper, we study the problem of finding the probability that the two-dimensional (biased) monotonic random walk crosses the line $y=αx+d$, where $α,d \geq 0$. A $β$-biased monotonic random walk moves from $(a,b)$ to $(a+1,b)$ or $(a,b+1)$ with probabilities $1/(β+ 1)$ and $β/(β+ 1)$, respectively. Among our results, we show that if $β\geq \lceil α\rceil$, then the $β$-biased monotonic random walk, starting from the origin, crosses the line $y=αx+d$ for all $d\geq 0$ with probability 1. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0709.3316 | |
| dc.identifier | http://arxiv.org/abs/0709.3316 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138478 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.subject | 60C05 | |
| dc.title | Line crossing problem for biased monotonic random walks in the plane | |
| dc.type | text |