TY - JOUR
T1 - On a Class of Stable Random Dynamical Systems
T2 - Theory and Applications
AU - Bhattacharya, Rabi
AU - Majumdar, Mukul
N1 - Funding Information:
1The research reported here was supported in part by NSF Grant DMS 9504557. We would like to thank a referee for helpful comments on earlier drafts.
PY - 2001/1
Y1 - 2001/1
N2 - 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 time-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, one is monotone, but the other is unimodal with two periodic points. Journal of Economic Literature Classification Numbers: C6, D9.
AB - 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 time-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, one is monotone, but the other is unimodal with two periodic points. Journal of Economic Literature Classification Numbers: C6, D9.
KW - Stability; dynamical systems; growth; cycles
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U2 - 10.1006/jeth.1999.2627
DO - 10.1006/jeth.1999.2627
M3 - Article
AN - SCOPUS:0012682611
SN - 0022-0531
VL - 96
SP - 208
EP - 229
JO - Journal of Economic Theory
JF - Journal of Economic Theory
IS - 1-2
ER -