Abstract
Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1=ɛn+1Xn(1−Xn), where ɛn are i.i.d. with values in the parameter space [0,4] of quadratic maps Fθ(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 Xn.
Citation
Rabi Bhattacharya. Mukul Majumdar. "Stability in distribution of randomly perturbed quadratic maps as Markov processes." Ann. Appl. Probab. 14 (4) 1802 - 1809, November 2004. https://doi.org/10.1214/105051604000000918
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