HAWKES PROCESSES ON LARGE NETWORKS

We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph G. The process is constructed as the solution to a system of Poisson driven stochastic differential equations, for which we prove pathwise existence and uniqueness...

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Veröffentlicht in:	The Annals of applied probability 2016-02, Vol.26 (1), p.216-261
Hauptverfasser:	Delattre, Sylvain, Fournier, Nicolas, Hoffmann, Marc
Format:	Artikel
Sprache:	eng
Schlagworte:	60F05 60G55 60G57 Approximation Central limit theorem Differential equations Infinity interacting particle systems Law of large numbers limit theorems Martingales Mathematics Matrices mean-field approximations multivariate Hawkes processes Point processes Poisson distribution Poisson process Probability distribution Random variables Scalars Statistics stochastic differential equations Stochastic models Uniqueness
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