Tangent Space Parametrization for Stochastic Differential Equations on SO(n)
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909582282981376 |
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| author | Wang, Xi Solo, Victor |
| author_facet | Wang, Xi Solo, Victor |
| contents | In this paper, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group $\text{SO}(n)$. We propose a geometry-preserving numerical scheme based on the stochastic tangent space parametrization (S-TaSP) method for state-dependent multiplicative SDEs on $\text{SO}(n)$. The convergence analysis of the S-TaSP scheme establishes a strong convergence order of $\mathcal{O}(δ^{\frac{1-ε}{2}})$, which matches the convergence order of the previous stochastic Lie Euler-Maruyama scheme while avoiding the computational cost of the exponential map. Numerical simulation illustrates the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12650 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tangent Space Parametrization for Stochastic Differential Equations on SO(n) Wang, Xi Solo, Victor Numerical Analysis In this paper, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group $\text{SO}(n)$. We propose a geometry-preserving numerical scheme based on the stochastic tangent space parametrization (S-TaSP) method for state-dependent multiplicative SDEs on $\text{SO}(n)$. The convergence analysis of the S-TaSP scheme establishes a strong convergence order of $\mathcal{O}(δ^{\frac{1-ε}{2}})$, which matches the convergence order of the previous stochastic Lie Euler-Maruyama scheme while avoiding the computational cost of the exponential map. Numerical simulation illustrates the theoretical results. |
| title | Tangent Space Parametrization for Stochastic Differential Equations on SO(n) |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.12650 |