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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/643| On the Asymptotic Behaviour of Increasing Self-Similar Markov Processes | |
| VICTOR MANUEL RIVERO MERCADO | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Procesos de Markov | |
| It has been proved by Bertoin and Caballero [8] that a1/α-increasing self-similar Markov process X is such that t−1/αX(t) converges weakly, ast → ∞, to a degenerated r.v. whenever the subordinator associated to it via Lamperti’s transformation has infinite mean. Here we prove thatlog(X(t)/t1/α)/log(t)converges in law to a non-degenerated r.v. if and only if the associated subordinator has Laplace exponent that varies regularly at 0. Moreover, we show that lim inft→∞log(X(t))/log(t) = 1/α,a.s. and provide an integraltest for the upper functions of{log(X(t)),t≥0}. Furthermore, results concerning the rate of growth of the random clock appearing in Lamperti’s transformation are obtained. In particular, these allow us to establish estimates for the left tail of some exponential functionals of subordinators. Finally, some of the implications of these results in the theory of self-similar fragmentations are discussed. | |
| Centro de Investigación en Matemáticas AC | |
| 13-11-2007 | |
| Reporte | |
| Inglés | |
| Investigadores | |
| PROCESOS DE MARKOV | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Reportes Técnicos - Probabilidad y Estadística |
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