Recently, Professor Cui Lirong and his collaborators published a research paper entitled "An elementary derivation of moments of Hawkes processes ""in Advances in Applied Probability. This paper presents an elementary method for solving the general conundrum (open question) of Hawkes process correlation moments. This method is not only effective for markov Hawkes processes, but also for some non-markov Hawkes processes. At the same time, the method extends the well-known Dynkin's formula for stochastic point processes.

　　Hawkes process is a kind of point process with self-excitation, which can describe cluster phenomenon and interaction well. Based on the background of earthquake aftershocks, proposed by British Professor A.G.Hawkes in 1971, it has been extended and applied in earthquake field. After more than 20 years of silence, in the 1990s, the Hawkes process began to receive widespread attention in the financial field. At present, in addition to earthquake and finance, it is widely used in social network, neuroscience, machine learning, reliability, information diffusion, crime prediction, insurance, patent citation, psychology, queuing theory, computer network transportation and so on.

　　Paper information: Cui,L.R.,Hawkes,A.G.,Yi H.(2020). An elementary derivation of moments of Hawkes processes.Adv.Appl. Prob .52,102-137..

　　Link: https://www.cambridge.org/core/journals/advances-in-applied-probability/article/an-elementary-derivation-of-moments-of-hawkes-processes/79A7355542F08087C8AE828C664A3049: