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

In this paper, we study the numerical simulation of stochastic differential equations (SDEs) on the special orthogonal Lie group . We propose a geometry-preserving numerical scheme based on the stochastic tangent space parametrization (S-TaSP) method for state-dependent multiplicative SDEs on . The convergence analysis of the S-TaSP scheme establishes a strong convergence order of (δ1-2), 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.