Adv. Math. Econ. Volume 2, pp.1-20 (2000)

Turnpike theorems for positive multivalued stochastic operators

S. V. Anoulova1, I. V. Evstingneev2 and V. M. Gundlach3
1 Institute for Control Science, Academy of Sciences of Russia, Profsoyuznaya 65, Moscow, 117806, Russia
2 Central Economics and Mathematics Institute, Academy of Sciences of Russia, Nakhimovsky 47, Moscow, 117418, Russia
3 Institute for Dynamical Systems,University of Bremen, Postfach 330440, 28334 Bremen, Germany
The paper analyzes the structure of paths of dynamical systems generated by positive multivalued mappings in spaces of random vectors. The primary focus is on "rapid" paths, growing in a certain sense faster than others. Their qualitative behavior over long or infinite time intervals is examined. The main results - turnpike theorems - state, in particular, that any two sufficiently long finite rapid paths are close to each other most of the time and any two infinite rapid paths converge to each other as the time parameter goes to infinity. The study is motivated by problems related to stochastic analogues of the von Neumann-Gale model of economic growth.