Hawkes process and Edgeworth expansion with application to maximum likelihood estimator

The Hawks process is a point with self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and getting lot of attention. However, as real problem, there are often situations where we can not obtain data sufficient observation time. In such cases, it appropriate approximate the error distribution an estimator by normal distribution. To overcome this provide rigorous mathematical foundation theory for higher-order asymptotic behavior one-dimensional Hawkes exponential kernel. As important application, give second-order maximum likelihood process. Furthermore, also present simulation results.