  Methods for proving functional limit laws are developed for sequences of
stochastic processes which allow a recursive distributional decomposition
either in time or space. Our approach is an extension of the so-called
contraction method to the space $\mathcal{C}[0,1]$ of continuous functions
endowed with uniform topology and the space $\mathcal {D}[0,1]$ of
c\`{a}dl\`{a}g functions with the Skorokhod topology. The contraction method
originated from the probabilistic analysis of algorithms and random trees where
characteristics satisfy natural distributional recurrences. It is based on
stochastic fixed-point equations, where probability metrics can be used to
obtain contraction properties and allow the application of Banach's fixed-point
theorem. We develop the use of the Zolotarev metrics on the spaces
$\mathcal{C}[0,1]$ and $\mathcal{D}[0,1]$ in this context. Applications are
given, in particular, a short proof of Donsker's functional limit theorem is
derived and recurrences arising in the probabilistic analysis of algorithms are
discussed.
