Journal of Applied Probability

On randomly spaced observations and continuous-time random walks

Bojan Basrak and Drago Špoljarić

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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.

Article information

J. Appl. Probab., Volume 53, Number 3 (2016), 888-898.

First available in Project Euclid: 13 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 60F17: Functional limit theorems; invariance principles 60G55: Point processes 60F05: Central limit and other weak theorems

Extreme value theory point process renewal process continuous-time random walk excursion sojourn time


Basrak, Bojan; Špoljarić, Drago. On randomly spaced observations and continuous-time random walks. J. Appl. Probab. 53 (2016), no. 3, 888--898.

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