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Affine Point Processes: Refinements to Large-Time Asymptotics

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 نشر من قبل Xuefeng Gao
 تاريخ النشر 2019
  مجال البحث
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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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