Error bound for the asymptotic expansion of the Hartman-Watson integral
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910905410781184 |
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| author | Pirjol, Dan |
| author_facet | Pirjol, Dan |
| contents | This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $θ(r,t)$ in the regime $rt=ρ$ constant. The leading order term has the form $θ(ρ/t,t)=\frac{1}{2πt}e^{-\frac{1}{t} (F(ρ)-π^2/2)} G(ρ) (1 + \vartheta(t,ρ))$, where the error term is bounded uniformly over $ρ$ as $|\vartheta(t,ρ)|\leq \frac{1}{70}t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error bound for the asymptotic expansion of the Hartman-Watson integral Pirjol, Dan Classical Analysis and ODEs Computational Finance This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $θ(r,t)$ in the regime $rt=ρ$ constant. The leading order term has the form $θ(ρ/t,t)=\frac{1}{2πt}e^{-\frac{1}{t} (F(ρ)-π^2/2)} G(ρ) (1 + \vartheta(t,ρ))$, where the error term is bounded uniformly over $ρ$ as $|\vartheta(t,ρ)|\leq \frac{1}{70}t$. |
| title | Error bound for the asymptotic expansion of the Hartman-Watson integral |
| topic | Classical Analysis and ODEs Computational Finance |
| url | https://arxiv.org/abs/2504.04992 |