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Global Sensitivity Analysis for Models Described by Stochastic Differential Equations

Author

Listed:
  • Pierre Étoré

    (Université Grenoble Alpes, CNRS, Inria, Grenoble INP (Institute of Engineering, Université Grenoble Alpes), LJK)

  • Clémentine Prieur

    (Université Grenoble Alpes, CNRS, Inria, Grenoble INP (Institute of Engineering, Université Grenoble Alpes), LJK)

  • Dang Khoi Pham

    (Université Grenoble Alpes, CNRS, Inria, Grenoble INP (Institute of Engineering, Université Grenoble Alpes), LJK)

  • Long Li

    (Université Grenoble Alpes, CNRS, Inria, Grenoble INP (Institute of Engineering, Université Grenoble Alpes), LJK)

Abstract

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.

Suggested Citation

  • Pierre Étoré & Clémentine Prieur & Dang Khoi Pham & Long Li, 2020. "Global Sensitivity Analysis for Models Described by Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 803-831, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09732-6
    DOI: 10.1007/s11009-019-09732-6
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    References listed on IDEAS

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    1. Le Maître, O.P. & Knio, O.M., 2015. "PC analysis of stochastic differential equations driven by Wiener noise," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 107-124.
    2. Iooss, Bertrand & Ribatet, Mathieu, 2009. "Global sensitivity analysis of computer models with functional inputs," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1194-1204.
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