Inverse problems for random walks on trees: network tomography
| dc.creator | de la Pena, Victor | |
| dc.creator | Gzyl, Henryk | |
| dc.creator | McDonald, Patrick | |
| dc.date | 2006-10-27 | |
| dc.date.accessioned | 2026-07-07T07:29:30Z | |
| dc.date.available | 2026-07-07T07:29:30Z | |
| dc.description | Let $G$ be a finite tree with root $r$ and associate to the internal vertices of $G$ a collection of transition probabilities for a simple nondegenerate Markov chain. Embedd $G$ into a graph $G^\prime$ constructed by gluing finite linear chains of length at least 2 to the terminal vertices of $G.$ Then $G^\prime$ admits distinguished boundary layers and the transition probabilities associated to the internal vertices of $G$ can be augmented to define a simple nondegenerate Markov chain $X$ on the vertices of $G^\prime.$ We show that the transition probabilities of $X$ can be recovered from the joint distribution of first hitting time and first hitting place of $X$ started at the root $r$ for the distinguished boundary layers of $G^\prime.$ | |
| dc.description | 11 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0610821 | |
| dc.identifier | http://arxiv.org/abs/math/0610821 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118135 | |
| dc.subject | Probability | |
| dc.subject | 60J10 (primary); 90B10 (secondary) | |
| dc.title | Inverse problems for random walks on trees: network tomography | |
| dc.type | text |