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

In this letter, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group $\text {SO}\text {(}n\text {)}$ . We propose a geometry-preserving numerical scheme based on the stochastic tangent space parametrization (S-TaSP) method for state-dependent multiplicative SDEs on $\text {SO}\text {(}n\text {)}$ . The convergence analysis of the S-TaSP scheme establishes a strong convergence order of ${\mathcal {O}}\text {(}\delta ^{{}\frac {1-\epsilon }{2}}\text {)}$ , which matches the convergence order of the previous stochastic Lie Euler-Maruyama scheme while avoiding the computational cost of the exponential map. Numerical simulations illustrate the theoretical results.