Construction and Simulation of Generalized Multivariate Hawkes Processes

Construction and Simulation of Generalized Multivariate Hawkes Processes

The main contribution of the paper amounts to providing a mathematical construction of a generalized multivariate Hawkes process (GMHP), as well as a simulation algorithm based on this construction. In particular, we justify the construction by demonstrating that the constructed process is indeed a...

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Veröffentlicht in:Methodology and computing in applied probability 2022-12, Vol.24 (4), p.2865-2896
Hauptverfasser: Bielecki, Tomasz R., Jakubowski, Jacek, Niewęgłowski, Mariusz
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Applied mathematics
Business and Management
Construction
Earthquakes
Economics
Electrical Engineering
Life Sciences
Mathematics and Statistics
Multivariate analysis
Random variables
Simulation
Statistics
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Zusammenfassung:The main contribution of the paper amounts to providing a mathematical construction of a generalized multivariate Hawkes process (GMHP), as well as a simulation algorithm based on this construction. In particular, we justify the construction by demonstrating that the constructed process is indeed a GMHP with desired properties. Towards this end we provide some new results regarding conditional Poisson random measures and doubly stochastic marked Poisson processes.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09934-5