Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence
Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence
复制标题
Kullback-Leibler 散度中小噪声扩散的高斯近似
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Stuart
中科院分区：
文献类型：
--
作者：
D. Sanz;A. Stuart
我们研究扩散分布的高斯近似。近似值很容易计算：它们由均值和协方差的两个简单常微分方程定义。时间相关性也可以通过线性随机微分方程的求解来计算。我们使用 Kullback-Leibler 散度证明了近似值在小噪声范围内是准确的。还研究了类似的离散时间设置。该结果既为在扩散近似中使用高斯过程提供了理论支持，也为在应用中构建高斯近似提供了方法指导。
We study Gaussian approximations to the distribution of a diffusion. The approximations are easy to compute: they are defined by two simple ordinary differential equations for the mean and the covariance. Time correlations can also be computed via solution of a linear stochastic differential equation. We show, using the Kullback-Leibler divergence, that the approximations are accurate in the small noise regime. An analogous discrete time setting is also studied. The results provide both theoretical support for the use of Gaussian processes in the approximation of diffusions, and methodological guidance in the construction of Gaussian approximations in applications.