Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest. One of the statistical tools used to quantify the influence of each input variable on the quantity of interest are the Sobol’ sensitivity indices. In this paper, we consider stochastic models described by stochastic differential equations (SDE). We focus the study on mean quantities, defined as the expectation with respect to the Wiener measure of a quantity of interest related to the solution of the SDE itself. Our approach is based on a Feynman-Kac representation of the quantity of interest, from which we get a parametrized partial differential equation (PDE) representation of our initial problem. We then handle the uncertainty on the parametrized PDE using polynomial chaos expansion and a stochastic Galerkin projection.

中文翻译：

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随机微分方程描述的模型的全局灵敏度分析

许多数学模型涉及输入参数，而这些参数尚不清楚。全局敏感性分析旨在确定不确定性对目标数量的可变性影响最大的参数。用于量化每个输入变量对所关注数量的影响的统计工具之一是Sobol灵敏度指数。在本文中，我们考虑用随机微分方程（SDE）描述的随机模型。我们将研究重点放在平均数量上，平均数量定义为对与SDE本身的解相关的感兴趣数量的维纳度量的期望。我们的方法基于感兴趣量的Feynman-Kac表示，从中我们得到了初始问题的参数化偏微分方程（PDE）表示。