Asymptotics for a Class of Self-Exciting Point Processes

2014/12/11 by Yang, Tzu-Wei, Zhu, Lingjiong
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1412.3771

Abstract

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.

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