On randomly spaced observations and continuous-time random walks (CROSBI ID 231377)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Basrak, Bojan ; Špoljarić, Drago
engleski
On randomly spaced observations and continuous-time random walks
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy-tailed steps, the limiting behavior of extreme observations until a given time t tends to be rather involved. We describe the asymptotics and extend several partial results which appeared in this setting. The theory is applied to determine the asymptotic distribution of maximal excursions and sojourn times for continuous-time random walks.
Extreme value theory ; point process ; renewal process ; continuous-time random walk ; excursion ; sojourn time
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Podaci o izdanju
53 (3)
2016.
888-898
objavljeno
0021-9002
1475-6072
10.1017/jpr.2016.47