Please use this identifier to cite or link to this item: 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
Appears in Collections:Reportes Técnicos - Probabilidad y Estadística

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