On randomly spaced observations and continuous-time random walks
Copyright policy )On randomly spaced observations and continuous-time random walks
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.
- University of Zagreb, Faculty of Science Croatia
- University of Zagreb Croatia
Functional limit theorems; invariance principles, 60G70, extreme value theory, renewal process, Extreme value theory, Probability (math.PR), Central limit and other weak theorems, Extreme value theory ; point process ; renewal process ; continuous-time random walk ; excursion ; sojourn time, Extreme value theory; extremal stochastic processes, 60G70 (Primary), 60F17, 60G55, 60F05 (Secondary), 60F17, 60F05, excursion, FOS: Mathematics, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), sojourn time, continuous-time random walk, Mathematics - Probability, point process
Functional limit theorems; invariance principles, 60G70, extreme value theory, renewal process, Extreme value theory, Probability (math.PR), Central limit and other weak theorems, Extreme value theory ; point process ; renewal process ; continuous-time random walk ; excursion ; sojourn time, Extreme value theory; extremal stochastic processes, 60G70 (Primary), 60F17, 60G55, 60F05 (Secondary), 60F17, 60F05, excursion, FOS: Mathematics, 60G55, Point processes (e.g., Poisson, Cox, Hawkes processes), sojourn time, continuous-time random walk, Mathematics - Probability, point process
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