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We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$.
The spectral analysis of point processes
M.S. Bartlett · 1963
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Point spectra of some mutually exciting point processes
A.G. Hawkes · 1971
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Spectra of some self-exciting and mutually exciting point processes
A.G. Hawkes · 1971
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Spectra of some mutually exciting point processes with associated variables
A.G. Hawkes · 1972
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A cluster process representation of a self-exciting process
A.G. Hawkes and D. Oakes · 1974
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Multivariate point processes: predictable projection, Radon-Nikodým derivatives, representation of martingales
J. Jacod · 1974
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The asymptotic behaviour of maximum likelihood estimators for stationary point processes
Y. Ogata · 1978
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Comovements in stock prices in the very short run
T. W. Epps · 1979
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On Lewis simulation method for point processes
Y. Ogata · 1981
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Limit theorems for stochastic processes
J. Jacod and A.N. Shiryaev · 1987
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Asymptotic Statistics
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Modeling financial contagion using mutually exciting jump processes
Y. Ait-Sahalia J. Cacho-Diaz and R. Laeven · 2011
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Multivariate Hawkes processes: an application to financial data
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