Affine Point Processes: Refinements to Large-Time Asymptotics
Probability
2019-07-26 v2
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.
Cite
@article{arxiv.1903.06371,
title = {Affine Point Processes: Refinements to Large-Time Asymptotics},
author = {Xuefeng Gao and Lingjiong Zhu},
journal= {arXiv preprint arXiv:1903.06371},
year = {2019}
}