Construction and Simulation of Generalized Multivariate Hawkes Processes

Tomasz R. Bielecki (), Jacek Jakubowski () and Mariusz Niewęgłowski ()
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Tomasz R. Bielecki: Illinois Institute of Technology
Jacek Jakubowski: University of Warsaw
Mariusz Niewęgłowski: Warsaw University of Technology

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2865-2896

Abstract: Abstract 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.

Keywords: Generalized multivariate Hawkes process; Simulation; Conditional Poisson random measures; Doubly stochastic marked Poisson process; 60G55; 60H99 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09934-5

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