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On randomly spaced observations and continuous-time random walks. J Appl Probab 2016. [DOI: 10.1017/jpr.2016.47] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
AbstractWe 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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Scalas E, Viles N. A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process. Stoch Process Their Appl 2014. [DOI: 10.1016/j.spa.2013.08.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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