# Quadrature methods for high-dimensional Gaussian integration

Suppose that $$f$$ is the density of a high(-$$d$$)-dimensional Gaussian measure with mean $$\mu$$ and non-singular covariance matrix $$\Sigma$$. Let $$g:\mathbb{R}^d\rightarrow \mathbb{R}$$ be a continuous function for which the integral $$\int f(x)g(x)dx<\infty$$.

Are there known "efficient" quadrature rules specifically for computing the integral $$\int f(x)g(x)dx$$ under these assumptions?