论文标题
Zakai方程有效的蒙特卡洛计划
An efficient Monte Carlo scheme for Zakai equations
论文作者
论文摘要
在本文中，我们开发了一种数值方法，用于在高维度上有效近似某些Zakai方程的解。关键思想是将给定的Zakai SPDE转换为具有随机系数的PDE。我们表明，在适当的规律性假设对Zakai方程的系数上的假设下，相应的随机PDE承认了一个解决方案随机场，几乎所有实现随机系数的实现都可以写成是线性抛物线PDE的经典解决方案。这使得可以应用Feynman-kac公式来获得有效的蒙特卡洛方案来计算Zakai方程的近似解决方案。该方法在快速运行时间的最多25个维度中取得了良好的效果。
In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai equation, the corresponding random PDE admits a solution random field which, for almost all realizations of the random coefficients, can be written as a classical solution of a linear parabolic PDE. This makes it possible to apply the Feynman--Kac formula to obtain an efficient Monte Carlo scheme for computing approximate solutions of Zakai equations. The approach achieves good results in up to 25 dimensions with fast run times.
