球面上布朗运动增量的模拟算法
An algorithm for simulating Brownian increments on a sphere
AI总结：
本文提出球面上布朗运动转移密度的新公式，并基于该公式与Wright-Fisher扩散的对偶性，开发了模拟球面布朗运动增量的算法，数值分析表明时间步长不太小时算法稳定。
摘要：
本文提出了任意维度球面上布朗运动转移密度的新公式，并讨论了一种基于该公式模拟球面布朗运动增量的算法。该密度公式源于一个观察：适当变换的径向过程（相对于测地距离）可被识别为Wright-Fisher扩散过程。此类过程与某种合并过程满足对偶性（一种对称性），这进而产生了转移密度的谱表示，利用Jenkins和Spanò（2017）的结果，该表示可用于精确模拟其增量。这种对称性进而产生了球面上布朗运动增量的模拟算法。我们对算法进行了数值分析，并表明当时间步长参数不太小时，该算法保持稳定。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
