  A result for subadditive ergodic cocycles is proved that provides more
delicate information than Kingman's subadditive ergodic theorem. As an
application we deduce a multiplicative ergodic theorem generalizing an earlier
result of Karlsson-Ledrappier, showing that the growth of a random product of
semi-contractions is always directed by some horofunction. We discuss
applications of this result to ergodic cocycles of bounded linear operators,
holomorphic maps and topical operators, as well as a random mean ergodic
theorem.
