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Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling-based method to determine evolution of uncertainty in a dynamical system, when there is probabilistic uncertainty in the system parameters. PC was first introduced by Norbert Wiener where Hermite polynomials were used to model stochastic processes with Gaussian random variables. It can be thought of as an extension of Volterra's theory of nonlinear functionals for stochastic systems. According to Cameron and Martin such an expansion converges in the

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  • Polynomial chaos
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  • Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling-based method to determine evolution of uncertainty in a dynamical system, when there is probabilistic uncertainty in the system parameters. PC was first introduced by Norbert Wiener where Hermite polynomials were used to model stochastic processes with Gaussian random variables. It can be thought of as an extension of Volterra's theory of nonlinear functionals for stochastic systems. According to Cameron and Martin such an expansion converges in the
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  • Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling-based method to determine evolution of uncertainty in a dynamical system, when there is probabilistic uncertainty in the system parameters. PC was first introduced by Norbert Wiener where Hermite polynomials were used to model stochastic processes with Gaussian random variables. It can be thought of as an extension of Volterra's theory of nonlinear functionals for stochastic systems. According to Cameron and Martin such an expansion converges in the sense for any arbitrary stochastic process with finite second moment. This applies to most physical systems.
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