论文标题
使用kolmogorov方程，非线性SDE的概率的数值计算
Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation
论文作者
论文摘要
考虑到具有随机偏微分方程（SPDE）的有限维近似结构的随机微分方程（SDE）。目的是通过求解相关的kolmogorov方程来计算与其解决方案相关的预期值和概率，并部分使用蒙特卡洛策略（确切地说，仅用于SDE的线性部分。基本思想是在JMAA（2020）的Flandoli等人中提出的，但是在这里我们通过辅助高斯过程的转移强烈改善了数值结果。对于相对简单的非线性，我们在100的顺序中具有良好的结果。
Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are considered. The aim is to compute numerically expected values and probabilities associated to their solutions, by solving the associated Kolmogorov equations, with a partial use of Monte Carlo strategy - precisely, using Monte Carlo only for the linear part of the SDE. The basic idea was presented in Flandoli et al., JMAA (2020), but here we strongly improve the numerical results by means of a shift of the auxiliary Gaussian process. For relatively simple nonlinearities, we have good results in dimension of the order of 100.
