Limit error distributions of Milstein scheme for stochastic Volterra equations with singular kernels
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912156883091456 |
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| author | Liu, Shanqi Hu, Yaozhong Gao, Hongjun |
| author_facet | Liu, Shanqi Hu, Yaozhong Gao, Hongjun |
| contents | For stochastic Volterra equations driven by standard Brownian and with singular kernels $K(u)=u^{H-\frac{1}{2}}/Γ(H+1/2), H\in (0,1/2)$, it is known that the Milstein scheme has a convergence rate of $n^{-2H}$. In this paper, we show that this rate is optimal. Moreover, we show that the error normalized by $n^{-2H}$ converge stably in law to the (nonzero) solution of a certain linear Volterra equation of random coefficients with the same fractional kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit error distributions of Milstein scheme for stochastic Volterra equations with singular kernels Liu, Shanqi Hu, Yaozhong Gao, Hongjun Probability For stochastic Volterra equations driven by standard Brownian and with singular kernels $K(u)=u^{H-\frac{1}{2}}/Γ(H+1/2), H\in (0,1/2)$, it is known that the Milstein scheme has a convergence rate of $n^{-2H}$. In this paper, we show that this rate is optimal. Moreover, we show that the error normalized by $n^{-2H}$ converge stably in law to the (nonzero) solution of a certain linear Volterra equation of random coefficients with the same fractional kernel. |
| title | Limit error distributions of Milstein scheme for stochastic Volterra equations with singular kernels |
| topic | Probability |
| url | https://arxiv.org/abs/2412.11126 |