Global sensitivity analysis for stochastic processes with independent increments
Résumé
This paper is a first attempt to develop a numerical technique
to analyze the sensitivity and the propagation of uncertainty
through a system with stochastic processes having independent increments
as input. Similar to Sobol’ indices for random variables, a metamodel
based on Chaos expansions is used and it is shown to be well
suited to address such problems. New global sensitivity indices are also
introduced to tackle the specificity of stochastic processes. The accuracy
and the efficiency of the proposed method is demonstrated on an analytical
example with three different input stochastic processes: a Wiener
process; an Ornstein-Uhlenbeck process and a Brownian bridge process.
The considered output, which is function of these three processes, is a
non-Gaussian process. Then, we apply the same ideas on an example
without known analytical solution.
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