Strong convergence of path sensitivities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912131779133440 |
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| author | Giles, Michael B. |
| author_facet | Giles, Michael B. |
| contents | It is well known that the Euler-Maruyama discretisation of an autonomous SDE using a uniform timestep $h$ has a strong convergence error which is $O(h^{1/2})$ when the drift and diffusion are both globally Lipschitz. This note proves that the same is true for the approximation of the path sensitivity to changes in a parameter affecting the drift and diffusion, assuming the appropriate number of derivatives exist and are bounded. This seems to fill a gap in the existing stochastic numerical analysis literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong convergence of path sensitivities Giles, Michael B. Numerical Analysis 65C05, 65C30 It is well known that the Euler-Maruyama discretisation of an autonomous SDE using a uniform timestep $h$ has a strong convergence error which is $O(h^{1/2})$ when the drift and diffusion are both globally Lipschitz. This note proves that the same is true for the approximation of the path sensitivity to changes in a parameter affecting the drift and diffusion, assuming the appropriate number of derivatives exist and are bounded. This seems to fill a gap in the existing stochastic numerical analysis literature. |
| title | Strong convergence of path sensitivities |
| topic | Numerical Analysis 65C05, 65C30 |
| url | https://arxiv.org/abs/2411.15930 |