论文标题
用于模拟球体上的布朗时增量的算法
An algorithm for simulating Brownian increments on a sphere
论文作者
论文摘要
本文提出了一个新的公式，用于在任何维度的球体上的布朗运动的过渡密度，并讨论了基于该公式的球形布朗运动增量的模拟算法。密度的公式来自观察，即可以将适当转化的径向过程（相对于地球距离）识别为Wright-Fisher扩散过程。这样的过程满足了与某个合并过程的二元性（一种对称性），而这又产生了过渡密度的光谱表示，可以使用Jenkins和Spanò（2017）的结果来精确模拟其增量。然后，对称性产生算法，以模拟球体上布朗运动的增量。我们通过数值分析算法，并表明当时间步参数不太小时，它保持稳定。
This paper presents a novel formula for the transition density of the Brownian motion on a sphere of any dimension and discusses an algorithm for the simulation of the increments of the spherical Brownian motion based on this formula. The formula for the density is derived from an observation that a suitably transformed radial process (with respect to the geodesic distance) can be identified as a Wright-Fisher diffusion process. Such processes satisfy a duality (a kind of symmetry) with a certain coalescent processes and this in turn yields a spectral representation of the transition density, which can be used for exact simulation of their increments using the results of Jenkins and Spanò (2017). The symmetry then yields the algorithm for the simulation of the increments of the Brownian motion on a sphere. We analyse the algorithm numerically and show that it remains stable when the time-step parameter is not too small.
