Lingjiong Zhu,  University of Minnesota-Twin Cities

Self-Exciting Point Processes

Self-exciting point processes are simple point processes that have been widely used in neuroscience, sociology, finance and many other fields. In many contexts, self-exciting point processes can model the complex systems in the real world better than the standard Poisson processes. We will discuss the Hawkes process, the most studied self-exciting point process in the literature and also propose a new model. Limit theorems, time asymptotics in different regimes, marginal and tail probabilities will be discussed. The second part of the talk is based on the joint work with Tzu-Wei Yang.