On a class of stable random dynamical systems: Theory and applications

• 成果类型: Article
• 署名作者: Bhattacharya, R; Majumdar, M
• 署名单位: Indiana University System; Indiana University Bloomington; Cornell University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.1999.2627
• 发表日期: 2001
• 页码: 208-229
• 关键词: stability; dynamical systems; GROWTH; cycles

摘要

We consider a random dynamical system in which the state space is an interval. and possible laws of motion are monotone functions. It is shown that if the Markov process generated by this system satisfies a splitting condition, it converges to a unique invariant distribution exponentially fast in the Kolmogorov distance. A central limit theorem on the lime-averages of observed values of the states is also proved. As an application we consider a system that captures an interaction of growth and cyclical forces: of two possible laws, on is monotone, but the other is unimodal with two periodic points. Journal of Economic Literature Classification Numbers: C6, D9. (C) 2001 Academic Press.