A polynomial chaos expansion in dependent random variables

Polynomial chaos expansion of a multimodal random vector

A methodology and algorithms are proposed for constructing the polynomial chaos expansion (PCE) of multimodal random vectors. An algorithm is developed for generating independent realizations of any multimodal multivariate probability measure that is constructed from a set of independent realizations using the Gaussian kernel-density estimation method. The PCE is then performed with respect to ...

Time-Dependent Polynomial Chaos

Conventional generalized polynomial chaos is known to fail for long time integration, loosing its optimal convergence behaviour and developing unacceptable error levels. The reason for this loss of convergence is the assumption that the probability density function is constant in time. By allowing a probability density function to evolve in time the optimal properties of polynomial chaos are re...

Central and Local Limit Theories in Markov Dependent Random Variables

Identification of random shapes from images through polynomial chaos expansion of random level-set functions

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