论文标题
从未知的扩散过程过渡密度取样
Sampling from Unknown Transition Densities of Diffusion processes
论文作者
论文摘要
在本文中，我们通过解决过渡密度的商满足的部分微分方程来介绍一种从扩散过程的过渡密度，包括封闭形式未知的新方法。我们证明了开发方法在具有已知密度的过程上的性能，并且获得的结果与理论值一致。该方法应用于赖特 - 法案扩散，因为它们在研究遗传数据中固有的相互作用网络中的重要性。有界漂移和非退化扩散的扩散过程被视为参考过程。 $ \ bf {关键单词}：$随机微分方程（SDE），过渡密度，fokker-Planck部分微分方程，Aronson的界限，拒绝采样，Wright-Fisher扩散。
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We demonstrate the performance of the developed method on processes with known densities and the obtained results are consistent with theoretical values. The method is applied to Wright-Fisher diffusions owing to their importance in population genetics in studying interaction networks inherent in genetic data. Diffusion processes with bounded drift and non degenerate diffusion are considered as reference processes. $\bf {Key words}:$ Stochastic differential equation (SDE), Transition density, Fokker-Planck partial differential equation, Aronson's bound, Rejection sampling, Wright-Fisher diffusion.
