Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes
Probability
2007-05-23 v1
Abstract
Iteration of randomly chosen quadratic maps defines a Markov process: X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with values in the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(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.
Cite
@article{arxiv.math/0503540,
title = {Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes},
author = {Rabi Bhattacharya and Mukul Majumdar},
journal= {arXiv preprint arXiv:math/0503540},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/105051604000000918 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)