Some limit theorems for Hawkes processes and application to financial statistics

@inproceedings{Bacry2013SomeLT,
  title={Some limit theorems for Hawkes processes and application to financial statistics},
  author={Emmanuel Bacry and Sylvain Delattre and Mikl{\'o}s Hoffmann and Jean-François Muzy},
  year={2013}
}
In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] when T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with mesh ∆ over [0, T ] up to some further time shift τ . The behaviour of this functional depends on… CONTINUE READING
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