An Explicit Euler-type Scheme for Lévy-driven SDEs with Superlinear and Time-Irregular Coefficients
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Biswas, Sani Fontbona, Joaquin |
| author_facet | Biswas, Sani Fontbona, Joaquin |
| contents | This paper introduces a randomized tamed Euler scheme tailored for Lévy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carathéodory-type drift. Under assumptions that allow for time-irregular drifts while ensuring appropriate time-regularity of the diffusion and jump coefficients, the proposed scheme is shown to achieve the optimal strong $\mathcal{L}^2$-convergence rate, arbitrarily close to $0.5$.
A crucial component of our methodology is the incorporation of drift randomization, which overcomes challenges due to low time-regularity, along with a taming technique to handle the superlinear state dependence.
Our analysis moreover covers settings where the coefficients are random, providing for instance strong convergence of randomized tamed Euler schemes for Lévy-driven stochastic delay differential equations (SDDEs) with Markovian switching. To our knowledge, this is the first {work} that addresses the case of superlinear coefficients in the numerical analysis of Carathéodory-type SDEs and even for ordinary differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18222 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Explicit Euler-type Scheme for Lévy-driven SDEs with Superlinear and Time-Irregular Coefficients Biswas, Sani Fontbona, Joaquin Numerical Analysis Probability This paper introduces a randomized tamed Euler scheme tailored for Lévy-driven stochastic differential equations (SDEs) with superlinear random coefficients and Carathéodory-type drift. Under assumptions that allow for time-irregular drifts while ensuring appropriate time-regularity of the diffusion and jump coefficients, the proposed scheme is shown to achieve the optimal strong $\mathcal{L}^2$-convergence rate, arbitrarily close to $0.5$. A crucial component of our methodology is the incorporation of drift randomization, which overcomes challenges due to low time-regularity, along with a taming technique to handle the superlinear state dependence. Our analysis moreover covers settings where the coefficients are random, providing for instance strong convergence of randomized tamed Euler schemes for Lévy-driven stochastic delay differential equations (SDDEs) with Markovian switching. To our knowledge, this is the first {work} that addresses the case of superlinear coefficients in the numerical analysis of Carathéodory-type SDEs and even for ordinary differential equations. |
| title | An Explicit Euler-type Scheme for Lévy-driven SDEs with Superlinear and Time-Irregular Coefficients |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2510.18222 |