Affine Point Processes: Refinements to Large-Time Asymptotics

2019/03/15 by Xuefeng Gao, Lingjiong Zhu, Gao, Xuefeng +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.06371

openalex publication_date 2019/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Multivariate Faa di Bruno Formula with Applications
• Sharp Large Deviations for the Ornstein--Uhlenbeck Process

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