  In this paper, we study a class of self-exciting point processes. The
intensity of the point process has a nonlinear dependence on the past history
and time. When a new jump occurs, the intensity increases and we expect more
jumps to come. Otherwise, the intensity decays. The model is a marriage between
stochasticity and dynamical system. In the short-term, stochasticity plays a
major role and in the long-term, dynamical system governs the limiting behavior
of the system. We study the law of large numbers, central limit theorem, large
deviations and asymptotics for the tail probabilities.
