  This paper presents a new numerical scheme for simulating stochastic
processes specified by their marginal distribution functions and covariance
functions. Stochastic samples are firstly generated to automatically satisfy
target marginal distribution functions. An iterative algorithm is proposed to
match the simulated covariance function of stochastic samples to the target
covariance function, and only a few times iterations can converge to a required
accuracy. Several explicit representations, based on Karhunen-Lo\`{e}ve
expansion and Polynomial Chaos expansion, are further developed to represent
the obtained stochastic samples in series forms. Proposed methods can be
applied to non-gaussian and non-stationary stochastic processes, and three
examples illustrate their accuracies and efficiencies.
