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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.15930 |
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Table of 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.