Tangent Space Parametrization for Stochastic Differential Equations on SO(n)
- 16 June 2025
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Control Systems Letters
- Vol. 9, 1369-1374
Abstract
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.Keywords
Funding Information
- Australian Research Council (DP220102159)
This publication has 15 references indexed in Scilit:
- Stratonovich, Ito and Numerical Analysis on Lie Groups2024
- Curved schemes for stochastic differential equations on, or near, manifoldsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022
- Higher strong order methods for linear Itô SDEs on matrix Lie groupsBIT Numerical Mathematics, 2022
- Convergence of a Tangent Space Numerical Scheme for a Stochastic Differential Equation on a Sphere2021
- Simultaneous Feedback and Feedforward Control and Its Application to Realize a Random Walk on the Bloch Sphere in an Xmon-Superconducting-Qubit SystemPhysical Review Applied, 2020
- Stochastic Models, Information Theory, and Lie Groups, Volume 22012
- Conservative stochastic differential equations: Mathematical and numerical analysisMathematics of Computation, 2009
- The optimal control problem on SO(4) and its applications to quantum controlIEEE Transactions on Automatic Control, 2002
- Stochastic Analysis on Manifolds2002
- An introduction to numerical methods for stochastic differential equationsActa Numerica, 1999