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首页> 外文会议>International Conference on Computational Science and Its Applications >Second Order Moments of Multivariate Hermite Polynomials in Correlated Random Variables
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Second Order Moments of Multivariate Hermite Polynomials in Correlated Random Variables

机译：相关随机变量中的多变量Hermite多项式的二阶矩

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Polynomial chaos methods can be used to estimate solutions of partial differential equations under uncertainty described by random variables. The stochastic solution is represented by a polynomial expansion, whose deterministic coefficient functions are recovered through Galerkin projections. In the presence of multiple uncertainties, the projection step introduces products (second order moments) of the basis polynomials. When the input random variables are correlated Gaussians, calculating the products of the corresponding multivariate basis polynomials is not straightforward and can become computationally expensive. We present a new expression for the products by introducing multiset notation for the polynomial indexing, which allows for simple and efficient evaluation of the second-order moments of correlated multivariate Hermite polynomials.
机译：多项式混沌方法可用于估计随机变量描述的不确定性下部分微分方程的解。 随机溶液由多项式膨胀表示，多项式膨胀，其确定性系数函数通过Galerkin投影恢复。 在存在多个不确定性的情况下，投影步骤引入了基础多项式的产品（二阶矩）。 当输入随机变量是相关的高斯，计算相应的多变量基础多项式的产品并不直接，并且可以变得昂贵。 我们通过对多项式索引引入多项式符号来提出新的表达式，这允许简单有效地评估相关多变量Hermite多项式的二阶矩。

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