Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes

Autor:	Horst, Ulrich, Xu, Wei
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematics - Functional Analysis Mathematics - Statistics Theory Primary 26A12 40E05 secondary 60G55 60K05
Druh dokumentu:	Working Paper
Popis:	This paper provides and extends second-order versions of several fundamental theorems on first-order regularly varying functions such as Karamata's theorem/representation and Tauberian's theorem. Our results are used to establish second-order approximations for the mean and variance of Hawkes processes with general kernels. Our approximations provide novel insights into the asymptotic behavior of Hawkes processes. They are also of key importance when establishing functional limit theorems for Hawkes processes. Comment: 39 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.02655 Zobrazit plný text záznamu View this record from Arxiv