  We report here on the recent application of a now classical general reduction
technique, the Reduced-Basis approach initiated in [C. Prud'homme, D. Rovas, K.
Veroy, Y. Maday, A. T. Patera, and G. Turinici. Reliable real-time solution of
parametrized partial differential equations: Reduced-basis output bounds
methods. Journal of Fluids Engineering, 124(1):7080, 2002.], to the specific
context of differential equations with random coefficients. After an elementary
presentation of the approach, we review two contributions of the authors: [S.
Boyaval, C. Le Bris, Y. Maday, N.C. Nguyen, and A.T. Patera. A reduced basis
approach for variational problems with stochastic parameters: Application to
heat conduction with variable Robin co-efficient. Computer Methods in Applied
Mechanics and Engineering, 198(4144):3187-3206, 2009.], which presents the
application of the RB approach for the discretization of a simple second order
elliptic equation supplied with a random boundary condition, and [S. Boyaval
and T. Leli\`evre, A variance reduction method for parametrized stochastic
differential equations using the reduced basis paradigm with T. Leli\`evre,
Commun. Math. Sci. 8, special Issue "Mathematical Issue on Complex Fluids" P.
Zhang ed., to appear, 2010, ARXIV preprint arXiv:0906.3600], which uses a RB
type approach to reduce the variance in the Monte-Carlo simulation of a
stochastic differential equation. We conclude the review with some general
comments and also discuss possible tracks for further research in the
direction.
