Rapid paths in von Neumann-Gale dynamical systems

Details Rapid paths in von Neumann-Gale dynamical systems Rapid paths in von Neumann-Gale dynamical systems

2007-12-20

arxiv.org/abs/0712.3353v1

Mathematics

Probability

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.i

Scientific paper

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.

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