| Título: | Convex minorants of random walks and Lévy processes |
| Autores: |
Abramson, Josh; University of California, Berkeley Pitman, Jim; University of California, Berkeley Ross, Nathan; University of California, Berkeley Uribe Bravo, Geronimo; Universidad Nacional Autónoma de México |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Random walks, Lévy processes, Brownian meander, Convex minorant, Uniform stick-breaking, Fluctuation theory 60G50,60G51 |
| Descripción: | This article provides an overview of recent work on descriptions and properties of the Convex minorants of random walks and Lévy processes, which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and Lévy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander. |
| Idioma: | No aplica |
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