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Autores principales: Horst, Ulrich, Xu, Wei
Formato: Preprint
Publicado: 2023
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Acceso en línea:https://arxiv.org/abs/2311.02655
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author Horst, Ulrich
Xu, Wei
author_facet Horst, Ulrich
Xu, Wei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2311_02655
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes
Horst, Ulrich
Xu, Wei
Probability
Functional Analysis
Statistics Theory
Primary 26A12, 40E05, secondary 60G55, 60K05
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.
title Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes
topic Probability
Functional Analysis
Statistics Theory
Primary 26A12, 40E05, secondary 60G55, 60K05
url https://arxiv.org/abs/2311.02655