Displaying similar documents to “One-dimensional diffusion in an asymmetric random environment”

Behavior near the extinction time in self-similar fragmentations I : the stable case

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...

Invariance principles for random walks conditioned to stay positive

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 𝒴 , i.e. there exists a sequence of positive real numbers ( ) such that / converges in law to 𝒴 . 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,...