Munich Personal RePEc Archive

Stochastic optimal growth with a non-compact state space

Zhang, Yuzhe (2007): Stochastic optimal growth with a non-compact state space. Published in: Journal of Mathematical Economics , Vol. 43, No. 2 (February 2007): pp. 115-129.

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Abstract

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [Brock,W.A., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory 4, 479–513] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

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