A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908441344212992 |
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| author | Vu, Thi-Huong Ngo, Hoang-Long Luong, Duc-Trong Khue, Tran Ngoc |
| author_facet | Vu, Thi-Huong Ngo, Hoang-Long Luong, Duc-Trong Khue, Tran Ngoc |
| contents | We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order $α$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+α)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients Vu, Thi-Huong Ngo, Hoang-Long Luong, Duc-Trong Khue, Tran Ngoc Probability Numerical Analysis We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally Hölder continuous of order $α$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+α)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients. |
| title | A tamed-adaptive Milstein scheme for stochastic differential equations with low regularity coefficients |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2411.01849 |