A generalized central limit theorem for critical marked Hawkes processes.

Prelegent(ci)

Anna Talarczyk-Noble

Afiliacja

Uniwersytet Warszawski

Język referatu

angielski

Termin

6 listopada 2025 12:15

Pokój

p. 3160

Tytuł w języku polskim

A generalized central limit theorem for critical marked Hawkes processes.

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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We study marked Hawkes processes in which occurrence of an event increases the intensity of future events by a certain base intensity function multiplied by an independent mark. We are particularly interested in the case when both the base intensity function and the law of the marks are heavy tailed and the mean number of events triggered by a single event is 1 (criticality). We discuss the relation of marked Hawkes processes with branching processes and prove a central limit type theorem for the process counting the number of events. In the limit we obtain an interesting long range dependent stable process.

 

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