Displaying similar documents to “Behavior near the extinction time in self-similar fragmentations I : the stable case”

The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation

Gerónimo Uribe Bravo (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We present a further analysis of the fragmentation at heights of the normalized brownian excursion. Specifically we study a representation for the mass of a tagged fragment in terms of a Doob transformation of the 1/2-stable subordinator and use it to study its jumps; this accounts for a description of how a typical fragment falls apart. These results carry over to the height fragmentation of the stable tree. Additionally, the sizes of the fragments in the brownian height fragmentation...

Penalisation of a stable Lévy process involving its one-sided supremum

Kouji Yano, Yuko Yano, Marc Yor (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Penalisation involving the one-sided supremum for a stable Lévy process with index ∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.

On suprema of Lévy processes and application in risk theory

Renming Song, Zoran Vondraček (2008)

Annales de l'I.H.P. Probabilités et statistiques

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Let =− where is a general one-dimensional Lévy process and an independent subordinator. Consider the times when a new supremum of is reached by a jump of the subordinator . We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and drifts to −∞, we decompose the absolute supremum of at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.

Refracted Lévy processes

A. E. Kyprianou, R. L. Loeffen (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation d =− { ...