Stochastic Monotonicity and Stationary Distributions for Dynamic Economies

The existence and stability of invariant distributions for stochastically monotone processes is studied. The Knaster-Tarski fixed point theorem is applied to establish existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering. Global...

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Veröffentlicht in:Econometrica. - Wiley. - 60(1992), 6, Seite 1387-1406
1. Verfasser: Hopenhayn, Hugo A. (VerfasserIn)
Weitere Verfasser: Prescott, Edward C.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1992
Zugriff auf das übergeordnete Werk:Econometrica
Schlagworte:Stationary distributions fixed points monotone functions stochastic dynamic programming stochastic growth theory investment theory Mathematics Philosophy Economics Behavioral sciences Social sciences
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520 |a The existence and stability of invariant distributions for stochastically monotone processes is studied. The Knaster-Tarski fixed point theorem is applied to establish existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering. Global convergence of a monotone Markov process to its unique invariant distribution is established under an easily verified assumption. Topkis' theory of supermodular functions is applied to stochastic dynamic optimization, providing conditions under which optimal stationary decisions are monotone functions of the state and induce a monotone Markov process. Applications of these results to investment theory, stochastic growth, and industry equilibrium dynamics are given. 
540 |a Copyright 1992 Econometric Society 
650 4 |a Stationary distributions 
650 4 |a fixed points 
650 4 |a monotone functions 
650 4 |a stochastic dynamic programming 
650 4 |a stochastic growth theory 
650 4 |a investment theory 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables  |x Stochastic processes  |x Markov processes 
650 4 |a Mathematics  |x Mathematical analysis  |x Mathematical monotonicity 
650 4 |a Philosophy  |x Metaphilosophy  |x Western philosophy  |x Continental philosophy  |x Structuralism  |x Conceptual structures  |x Conceptual lattices 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions 
650 4 |a Economics  |x Economic disciplines  |x Financial economics  |x Finance  |x Financial instruments  |x Financial securities  |x Capital stocks 
650 4 |a Economics  |x Economic theory 
650 4 |a Philosophy  |x Logic  |x Logical topics  |x Formal logic  |x Mathematical logic  |x Mathematical set theory  |x Mathematical sets  |x Partially ordered sets 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Decision making  |x Optimal policy 
650 4 |a Social sciences  |x Development studies  |x Development economics  |x Economic development  |x Economic growth  |x Economic growth theories 
650 4 |a Philosophy  |x Metaphysics  |x Ontology  |x Ontological properties  |x Uniqueness 
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700 1 |a Prescott, Edward C.  |e verfasserin  |4 aut 
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