A Randomized Milstein Scheme for SDEs with Superlinear Drift Coefficient
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908765063741440 |
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| author | Biswas, Sani |
| author_facet | Biswas, Sani |
| contents | This work presents a randomized-tamed Milstein scheme for stochastic differential equations whose drift coefficient exhibits superlinear growth in the state variable and limited temporal regularity, quantified by $β$-Hölder continuity with $β\in (0,1]$. The scheme combines a taming mechanism to control the superlinear state dependence with a drift randomization strategy designed to address the challenges posed by low temporal regularity. Under suitable assumptions on temporal smoothness, the scheme achieves an optimal strong $\mathscr{L}^p$-convergence rate of order one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Randomized Milstein Scheme for SDEs with Superlinear Drift Coefficient Biswas, Sani Numerical Analysis Probability 65C30, 60H35, 65C05, 65C35 This work presents a randomized-tamed Milstein scheme for stochastic differential equations whose drift coefficient exhibits superlinear growth in the state variable and limited temporal regularity, quantified by $β$-Hölder continuity with $β\in (0,1]$. The scheme combines a taming mechanism to control the superlinear state dependence with a drift randomization strategy designed to address the challenges posed by low temporal regularity. Under suitable assumptions on temporal smoothness, the scheme achieves an optimal strong $\mathscr{L}^p$-convergence rate of order one. |
| title | A Randomized Milstein Scheme for SDEs with Superlinear Drift Coefficient |
| topic | Numerical Analysis Probability 65C30, 60H35, 65C05, 65C35 |
| url | https://arxiv.org/abs/2601.09437 |