Displaying similar documents to “Sinaıˇ's condition for real valued Lévy processes”

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,...