  The paper examines random dynamical systems related to the classical von
Neumann and Gale models of economic growth. Such systems are defined in terms
of multivalued operators in spaces of random vectors, possessing certain
properties of convexity and homogeneity. A central role in the theory of von
Neumann-Gale dynamics is played by a special class of paths called rapid (they
maximize properly defined growth rates). Up to now the theory lacked quite
satisfactory results on the existence of such paths. This work provides a
general existence theorem holding under assumptions analogous to the standard
deterministic ones. The result solves a problem that remained open for more
than three decades.
