2017/02/28 by Fuqing Gao, Lingjiong Zhu · 1 citation
Mathematics · #math.PR
published as Stochastic Processes and their Applications 2018, Volume 128, Issue 12, 4051-4077 · 33 pages
arxiv created 2017/11/21 · arxiv updated 2018/11/05
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study fluctuations, large deviations and moderate deviations nonlinear Hawkes processes in a new asymptotic regime, the large intensity function and the small exciting function regime. It corresponds to the large baseline intensity asymptotics for the linear case, and can also be interpreted as the asymptotics for the mean process of Hawkes processes on a large network.