Second-Order Regular Variation and Second-Order Approximation of Hawkes Processes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910817673281536 |
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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 |