Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes
Abstract
Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1=εn+1Xn(1-Xn), where εn are i.i.d. with values in the parameter space [0,4] of quadratic maps Fθ(x)=θ 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 Xn.
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