Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

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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.
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)

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Probability, 60J05 (Primary) 60J20, 37H10. (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/74636

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503540
 http://arxiv.org/abs/math/0503540
 Annals of Applied Probability 2004, Vol. 14, No. 4, 1802-1809
 doi:10.1214/105051604000000918

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arXiv