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On extreme value asymptotics for increments of renewal processes. (English) Zbl 0831.60060
The authors consider the problem of detecting changes in the intensity of a general renewal counting process. Their main idea is to consider increments of the process rather than the process itself, and to compare the maximum deviation between empirical intensities over subsequent small intervals or between small intervals in the beginning and the whole range, respectively. They prove a number of limit theorems for increments of renewal processes under the null hypothesis of no change in intensity. The paper also gives tables of Monte Carlo estimates of selected percentiles of limiting distribution functions of four sup-functionals proposed for testing change in intensity.

##### MSC:
 60G70 Extreme value theory; extremal stochastic processes 60F05 Central limit and other weak theorems 60K05 Renewal theory 60F17 Functional limit theorems; invariance principles
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##### References:
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