  Let $X_n$ be independent random elements in the Skorohod space $D([0,1];E)$
of c\`{a}dl\`{a}g functions taking values in a separable Banach space $E$. Let
$S_n=\sum_{j=1}^nX_j$. We show that if $S_n$ converges in finite dimensional
distributions to a c\`{a}dl\`{a}g process, then $S_n+y_n$ converges a.s.
pathwise uniformly over $[0,1]$, for some $y_n\in D([0,1];E)$. This result
extends the It\^{o}-Nisio theorem to the space $D([0,1];E)$, which is
surprisingly lacking in the literature even for $E=R$. The main difficulties of
dealing with $D([0,1];E)$ in this context are its nonseparability under the
uniform norm and the discontinuity of addition under Skorohod's $J_1$-topology.
We use this result to prove the uniform convergence of various series
representations of c\`{a}dl\`{a}g infinitely divisible processes. As a
consequence, we obtain explicit representations of the jump process, and of
related path functionals, in a general non-Markovian setting. Finally, we
illustrate our results on an example of stable processes. To this aim we obtain
new criteria for such processes to have c\`{a}dl\`{a}g modifications, which may
also be of independent interest.

Probability