Displaying similar documents to “The strong law of large numbers for dependent vector processes with decreasing correlation: “Double averaging concept”.”

On fully coupled continuous time random walks

W. Szczotka, P. Żebrowski (2012)

Applicationes Mathematicae

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Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.

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,...