Article ID Journal Published Year Pages File Type
5488178 Chinese Journal of Physics 2017 27 Pages PDF
Abstract
We show, under wide hypothesis, that the problem of forward propagation of uncertainties in a physical model reduces to a well known problem in probability theory: the determination of the weighted sum of N independent stochastic variables obeying arbitrary distributions supported on bounded intervals. We determine various exact expressions for the probability distribution of the sum, possibly weighted, of N independent stochastic variables obeying arbitrary polynomial distributions on different intervals. These exact results provide the mathematical basis for the treatment of the given problem. We discuss the relevance of these findings for parameter uncertainty quantification in the context of particle transport computations. As a byproduct an explicit formula for the convolution of an arbitrary number of polynomials supported on bounded intervals is obtained.
Related Topics
Physical Sciences and Engineering Physics and Astronomy Atomic and Molecular Physics, and Optics
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