Limits of renewal processes and Pitman-Yor distribution (CROSBI ID 231375)
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Podaci o odgovornosti
Basrak, Bojan
engleski
Limits of renewal processes and Pitman-Yor distribution
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time t, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time t, they converge after scaling to the Pitman–Yor distribution. We further discuss how our results extend the classical Dynkin–Lamperti theorem.
Dynkin–Lamperti theorem ; invariance principle ; Pitman–Yor distribution ; point process ; renewal process ; regular variation
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