The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.
"Central limit theorem for nonlinear Hawkes processes." J. Appl. Probab. 50 (3) 760 - 771, September 2013. https://doi.org/10.1239/jap/1378401234