Tangent Space Parametrization for Stochastic Differential Equations on SO(n)

Xi Wang; Victor Solo

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arXiv · 2504.12650

Tangent Space Parametrization for Stochastic Differential Equations on SO(n)

Xi Wang·Victor Solo

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Abstract

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 $\mathcal{O}(\delta^{\frac{1-\epsilon}{2}})$, 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.

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Xi Wang, Victor Solo. 2025-04-17. Tangent Space Parametrization for Stochastic Differential Equations on SO(n). https://arxiv.org/abs/2504.12650

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