Strong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918379140415488 |
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| author | Schwarz, Verena |
| author_facet | Schwarz, Verena |
| contents | We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Milstein scheme is the first scheme that has strong convergence rate $1$ in terms of the number of evaluations of the driving noise processes in $L^p$ for $p\in[1,\infty)$. To obtain our result, we prove that under slightly stronger assumptions, which are still weaker than those in the existing literature, a related doubly-adaptive quasi-Milstein scheme has convergence order $1$. This scheme is doubly-adaptive in the sense that it is jump-adapted, i.e. all jump times of the Poisson noise are grid points, and it includes an adaptive step-size strategy to account for the discontinuities of the drift. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift Schwarz, Verena Numerical Analysis Probability 60H10, 65C30, 65C20 We present an adaptive approximation scheme for jump-diffusion SDEs with discontinuous drift and (possibly) degenerate diffusion. This transformation-based doubly-adaptive quasi-Milstein scheme is the first scheme that has strong convergence rate $1$ in terms of the number of evaluations of the driving noise processes in $L^p$ for $p\in[1,\infty)$. To obtain our result, we prove that under slightly stronger assumptions, which are still weaker than those in the existing literature, a related doubly-adaptive quasi-Milstein scheme has convergence order $1$. This scheme is doubly-adaptive in the sense that it is jump-adapted, i.e. all jump times of the Poisson noise are grid points, and it includes an adaptive step-size strategy to account for the discontinuities of the drift. |
| title | Strong order 1 adaptive approximation of jump-diffusion SDEs with discontinuous drift |
| topic | Numerical Analysis Probability 60H10, 65C30, 65C20 |
| url | https://arxiv.org/abs/2504.09452 |