Abstract
Iteration of randomly chosen quadratic maps defines a Markov process: X n+1 = ε n+1 X n(1 - X n), where ε n are i.i.d. with values in the parameter space [0,4] of quadratic maps F θ(x) = θx(1 - x). Its study is of significance as an important Markov model, with applications to problems of optimization under uncertainty arising in economics. In this article a broad criterion is established for positive Harris recurrence of X n.
Original language | English (US) |
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Pages (from-to) | 1802-1809 |
Number of pages | 8 |
Journal | Annals of Applied Probability |
Volume | 14 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2004 |
Externally published | Yes |
Keywords
- Invariant probability
- Markov process
- Quadratic maps
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty