“…Hawkes processes have been widely used to model various applications, for example, in finance [2,11] and internet traffic and queueing [4,6,7,14]. There are extensive studies of Hawkes processes, including the exact distributional properties [12,16] for exponential-type kernel functions, and limit theorems in both conventional scaling [1,2,4,13] and large-intensity scaling [7,8,15].…”