  In this manuscript we propose and analyze weighted reduced order methods for
stochastic Stokes and Navier-Stokes problems depending on random input data
(such as forcing terms, physical or geometrical coefficients, boundary
conditions). We will compare weighted methods such as weighted greedy and
weighted POD with non-weighted ones in case of stochastic parameters. In
addition we will analyze different sampling and weighting choices to overcome
the curse of dimensionality with high dimensional parameter spaces.
