We present a scheme for simulating conditioned semimartingales taking values in Riemannian manifolds. Extending the guided bridge proposal approach used for simulating Euclidean bridges, the scheme replaces the drift of the conditioned process with an approximation in terms of a scaled radial vector field. This handles the fact that transition densities are generally intractable on geometric spaces. We prove the validity of the scheme by a change of measure argument, and we show how the resulting guided processes can be used in importance sampling and for approximating the density of the unconditioned process. The scheme is used for numerically simulating bridges on two- and three-dimensional manifolds, for approximating otherwise intractable transition densities, and for estimating the diffusion mean of sampled geometric data.

翻译：我们提出了一种用于模拟取值于黎曼流形的条件半鞅的方案。该方案将用于模拟欧几里得桥的引导桥提议方法进行扩展，通过基于缩放径向向量场的近似替换条件过程的漂移项，从而解决了几何空间中转移密度通常难以处理的问题。我们通过测度变换论证证明了该方案的有效性，并展示了如何将生成的引导过程应用于重要性采样以及近似无条件过程的密度。该方案被用于二维和三维流形上的数值桥模拟、近似其他难以处理的转移密度，以及估计采样几何数据的扩散均值。