Proves convergence in law of normalized empirical measures and counting processes for critical marked Hawkes processes to stable or Gaussian limits depending on mark tail behavior, using a new robust method for self-exciting systems.
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For small β, the normalized event counting process of critical marked Hawkes processes with (1+β)-stable marks converges in law to a spectrally positive 1/(1+β)-stable Lévy process in Skorokhod M1 topology.
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A generalized central limit theorem for critical marked Hawkes processes
Proves convergence in law of normalized empirical measures and counting processes for critical marked Hawkes processes to stable or Gaussian limits depending on mark tail behavior, using a new robust method for self-exciting systems.
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Large time behavior of critical marked Hawkes processes with heavy tailed marks and related branching particle systems
For small β, the normalized event counting process of critical marked Hawkes processes with (1+β)-stable marks converges in law to a spectrally positive 1/(1+β)-stable Lévy process in Skorokhod M1 topology.