Jump amplitude inference in SDEs with cosine kernel
For estimating the jump amplitude in stochastic differential equations with jumps, existing parameter estimation methods in the academic community suffer from inherent systematic errors. Commonly used kernel functions often assume symmetric distributions, limiting their ability to model skewed distr...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2025-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000603 |
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| _version_ | 1849722146316615680 |
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| author | Wuchen Li Luwen Zhang Jian Xu Linghui Li Liping Bai |
| author_facet | Wuchen Li Luwen Zhang Jian Xu Linghui Li Liping Bai |
| author_sort | Wuchen Li |
| collection | DOAJ |
| description | For estimating the jump amplitude in stochastic differential equations with jumps, existing parameter estimation methods in the academic community suffer from inherent systematic errors. Commonly used kernel functions often assume symmetric distributions, limiting their ability to model skewed distributions. Many methods can simulate positively skewed distributions but fail to handle negatively skewed ones, and they tend to overestimate the probability density when the jump size is close to zero. This paper introduces a novel kernel density estimation method based on cosine functions for jump amplitude estimation. Our approach addresses these systematic errors, especially under large sample conditions, enabling more accurate statistical inference for the jump amplitude in stochastic differential equations with jumps. We anticipate that this method will contribute positively to research in areas such as finance and signal processing. |
| format | Article |
| id | doaj-art-a3eb0156a1e34e1083341930a63cfcc4 |
| institution | DOAJ |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-a3eb0156a1e34e1083341930a63cfcc42025-08-20T03:11:26ZengElsevierResults in Applied Mathematics2590-03742025-05-012610059610.1016/j.rinam.2025.100596Jump amplitude inference in SDEs with cosine kernelWuchen Li0Luwen Zhang1Jian Xu2Linghui Li3Liping Bai4Macau University of Science and Technology, MacauMacau University of Science and Technology, MacauSouth China University of Technology, ChinaMacau University of Science and Technology, MacauFaculty of Innovation Engineering, Macau University of Science and Technology, Macau; Corresponding author.For estimating the jump amplitude in stochastic differential equations with jumps, existing parameter estimation methods in the academic community suffer from inherent systematic errors. Commonly used kernel functions often assume symmetric distributions, limiting their ability to model skewed distributions. Many methods can simulate positively skewed distributions but fail to handle negatively skewed ones, and they tend to overestimate the probability density when the jump size is close to zero. This paper introduces a novel kernel density estimation method based on cosine functions for jump amplitude estimation. Our approach addresses these systematic errors, especially under large sample conditions, enabling more accurate statistical inference for the jump amplitude in stochastic differential equations with jumps. We anticipate that this method will contribute positively to research in areas such as finance and signal processing.http://www.sciencedirect.com/science/article/pii/S2590037425000603Stochastic differential equationsJump amplitudeSystematic errorCosine kernelKernel density estimation function |
| spellingShingle | Wuchen Li Luwen Zhang Jian Xu Linghui Li Liping Bai Jump amplitude inference in SDEs with cosine kernel Results in Applied Mathematics Stochastic differential equations Jump amplitude Systematic error Cosine kernel Kernel density estimation function |
| title | Jump amplitude inference in SDEs with cosine kernel |
| title_full | Jump amplitude inference in SDEs with cosine kernel |
| title_fullStr | Jump amplitude inference in SDEs with cosine kernel |
| title_full_unstemmed | Jump amplitude inference in SDEs with cosine kernel |
| title_short | Jump amplitude inference in SDEs with cosine kernel |
| title_sort | jump amplitude inference in sdes with cosine kernel |
| topic | Stochastic differential equations Jump amplitude Systematic error Cosine kernel Kernel density estimation function |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000603 |
| work_keys_str_mv | AT wuchenli jumpamplitudeinferenceinsdeswithcosinekernel AT luwenzhang jumpamplitudeinferenceinsdeswithcosinekernel AT jianxu jumpamplitudeinferenceinsdeswithcosinekernel AT linghuili jumpamplitudeinferenceinsdeswithcosinekernel AT lipingbai jumpamplitudeinferenceinsdeswithcosinekernel |