Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

Details Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

2005-03-24

arxiv.org/abs/math/0503540v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1802-1809

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000918 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000918

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.

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