Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909954034630656 |
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| author | Fukuda, Ikki Kagaya, Yoshiki Ueda, Yuki |
| author_facet | Fukuda, Ikki Kagaya, Yoshiki Ueda, Yuki |
| contents | We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous results including Laplace's method. The key points of the proof are a precise asymptotic analysis based on a lot of detailed Taylor expansions, and a careful consideration of the effects of the perturbations on the Hessian matrix of the phase function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations Fukuda, Ikki Kagaya, Yoshiki Ueda, Yuki Classical Analysis and ODEs Probability 41A60, 41A80 We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous results including Laplace's method. The key points of the proof are a precise asymptotic analysis based on a lot of detailed Taylor expansions, and a careful consideration of the effects of the perturbations on the Hessian matrix of the phase function. |
| title | Higher-order asymptotic expansion with error estimate for the multidimensional Laplace-type integral under perturbations |
| topic | Classical Analysis and ODEs Probability 41A60, 41A80 |
| url | https://arxiv.org/abs/2504.01310 |