Generalized Decoupled Polynomial Chaos for Nonlinear Circuits With Many Random Parameters

Polynomial Chaos for Linear Differential Algebraic Equations with Random Parameters

Technical applications are often modeled by systems of differential algebraic equations. The systems may include parameters that involve some uncertainties. We arrange a stochastic model for uncertainty quantification in the case of linear systems of differential algebraic equations. The generalized polynomial chaos yields a larger linear system of differential algebraic equations, whose soluti...

Generalized polynomial chaos and random oscillators

We present a new approach to obtain solutions for general random oscillators using a broad class of polynomial chaos expansions, which are more efficient than the classical Wiener–Hermite expansions. The approach is general but here we present results for linear oscillators only with random forcing or random coefficients. In this context, we are able to obtain relatively sharp error estimates i...

Time-dependent generalized polynomial chaos

Article history: Received 11 May 2009 Received in revised form 11 June 2010 Accepted 21 July 2010 Available online 13 August 2010

Polynomial chaos for simulating random volatilities

In financial mathematics, the fair price of options can be achieved by solutions of parabolic differential equations. The volatility usually enters the model as a constant parameter. However, since this constant has to be estimated with respect to the underlying market, it makes sense to replace the volatility by an according random variable. Consequently, a differential equation with stochasti...

Classification Algorithms based on Generalized Polynomial Chaos