Central Limit Theorem for Nonlinear Hawkes Processes

Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the contrary, nonlinear Hawkes process lacks the immigrationbirth representation and is much harder to analyze. In this paper, we obtain a functional central limit theorem for nonlinear Hawkes process.