Affine Point Processes: Refinements to Large-Time Asymptotics

Xuefeng Gao; Lingjiong Zhu

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arXiv · 1903.06371

Affine Point Processes: Refinements to Large-Time Asymptotics

Xuefeng Gao·Lingjiong Zhu

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Abstract

Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large deviations and refined central limit theorem for affine point processes, using the framework of mod-phi convergence. Our results extend the large-time limit theorems in [Zhang et al. 2015. Math. Oper. Res. 40(4), 797-819]. The resulting explicit approximations for large deviation probabilities and tail expectations can be used as an alternative to importance sampling Monte Carlo simulations. Numerical experiments illustrate our results.

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Xuefeng Gao, Lingjiong Zhu. 2019-03-15. Affine Point Processes: Refinements to Large-Time Asymptotics. https://arxiv.org/abs/1903.06371

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