Diffusions in random environment and ballistic behavior
Tom Schmitz (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Tom Schmitz (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Christina Goldschmidt, Bénédicte Haas (2010)
Annales de l'I.H.P. Probabilités et statistiques
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The stable fragmentation with index of self-similarity ∈[−1/2, 0) is derived by looking at the masses of the subtrees formed by discarding the parts of a (1+)−1–stable continuum random tree below height , for ≥0. We give a detailed limiting description of the distribution of such a fragmentation, ((), ≥0), as it approaches its time of extinction, . In particular, we show that 1/ ((−)+) converges in distribution as →0 to a non-trivial limit. In order to prove this, we go...
L. C. G. Rogers (1984)
Séminaire de probabilités de Strasbourg
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Engländer, János (2007)
Probability Surveys [electronic only]
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Francesco Caravenna, Loïc Chaumont (2008)
Annales de l'I.H.P. Probabilités et statistiques
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Let { be a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( ) such that / converges in law to . Our main result is that the rescaled process ( / , ≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions,...
Amir Dembo, Jean-Dominique Deuschel (2007)
Annales de l'I.H.P. Probabilités et statistiques
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