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Large deviations of Poisson cluster processes. (English) Zbl 1152.60316
Summary: We prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.

MSC:
60F10 Large deviations
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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