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Invariance principles for random walks conditioned to stay positive

Francesco Caravenna, Loïc Chaumont (2008)

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

Let {Snbe a random walk in the domain of attraction of a stable law 𝒴 , i.e. there exists a sequence of positive real numbers ( an) such that Sn/anconverges in law to 𝒴 . Our main result is that the rescaled process (S⌊nt⌋/an, t≥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, we also prove a related invariance principle for the random walk killed at its first...

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