$α$-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916905395159040 |
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| author | Chen, Jingwei |
| author_facet | Chen, Jingwei |
| contents | This paper develops an $α$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs) with time-space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of $min\{η_{F},η_{G},η_{H},α/2\}$, establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and would facilitate applications in finance and biology where time-changed Lévy models are prevalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $α$-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity Chen, Jingwei Probability Numerical Analysis 65C30, 60H10 This paper develops an $α$-parametrized framework for analyzing the strong convergence of the stochastic theta (ST) method for stochastic differential equations driven by time-changed Lévy noise (TCSDEwLNs) with time-space-dependent coefficients satisfying local Lipschitz conditions. Properties of the inverse subordinator are investigated and explicit moment bounds for the exact solution are derived with jump rate incorporated. The analysis demonstrates that the ST method converges strongly with order of $min\{η_{F},η_{G},η_{H},α/2\}$, establishing a precise relationship between numerical accuracy and the time-change mechanism. This theoretical advancement extends existing results and would facilitate applications in finance and biology where time-changed Lévy models are prevalent. |
| title | $α$-scaled strong convergence of stochastic theta method for stochastic differential equations driven by time-changed Lévy noise beyond Lipschitz continuity |
| topic | Probability Numerical Analysis 65C30, 60H10 |
| url | https://arxiv.org/abs/2508.12909 |