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Limits of renewal processes and Pitman-Yor distribution (CROSBI ID 231375)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Basrak, Bojan Limits of renewal processes and Pitman-Yor distribution // Electronic communications in probability, 20 (2015), 51, 13. doi: 10.1214/ECP.v20-4080

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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Podaci o izdanju

20

2015.

51

13

objavljeno

1083-589X

10.1214/ECP.v20-4080

Povezanost rada

Matematika

Poveznice
Indeksiranost