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September 2016 On randomly spaced observations and continuous-time random walks
Bojan Basrak, Drago Špoljarić
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J. Appl. Probab. 53(3): 888-898 (September 2016).

Abstract

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.

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Bojan Basrak. Drago Špoljarić. "On randomly spaced observations and continuous-time random walks." J. Appl. Probab. 53 (3) 888 - 898, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60066
MathSciNet: MR3570101

Subjects:
Primary: 60G70
Secondary: 60F05 , 60F17 , 60G55

Keywords: Continuous-time random walk , excursion , Extreme value theory , point process , Renewal process , sojourn time

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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