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Stochastic numerical analysis for Brownian motion on SO(3)

Traditional methods for simulating stochastic differential equations fail when applied to processes evolving in manifolds as these schemes leave the manifold, often after a single time step. In the deterministic case the geometric numerical integration literature is well established, but for stochastic differential equations in manifolds the literature is sparse and underdeveloped. In this paper, we construct a simple geometric Euler numerical scheme for simulating Brownian motion on SO(3) and study its uniform mean square convergence to the underlying stochastic differential equation. Simulations are provided which illustrate the preservation of the manifold structure.