2021/04/01 by Tien Cuong Phi, Eva Löcherbach, Phi, Tien Cuong +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #60G55 #60K35 #Diffusion and Search Dynamics #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2104.00495
openalex publication_date 2021/04/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a finite network and with empty past before 0. The Kalikow decomposition is not unique and we discuss the choice of the decomposition in terms of algorithmic efficiency in certain cases. We apply these methods on several examples: linear Hawkes process, age dependent Hawkes process, exponential Hawkes process, Galves-Löcherbach process.