This paper is makes sophisticated contributions on the theoretical and methodological fronts along with an interesting practical example. These network process models are fairly difficult to handle probabilistically and the continuous-time methods developed here are quite rigorous. The reviewers raised some concerns about comparisons to Bayesian nonparametric approaches (esp. R2) but I agree with the authors response that this paper develops a fairly different frequentist framework that is complementary to existing approaches in both their theoretical validity and computational efficiency. However, I do concur with R2 that some simulations should be added that verify coverage for small T, but this does not require a resubmission and can be added for the final version. All reviewers agreed that this work is novel and would be of interest to researchers employing Hawkes processes, and in my judgment R2 was slightly harsh with the final score. I recommend the authors to take the couple of suggestions into account (eg: experiments for small T), in order to strengthen an already very nice paper.