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Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

Rabi Bhattacharya·Mukul Majumdar
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Abstract

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.

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Rabi Bhattacharya, Mukul Majumdar. 2005-03-24. Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes. https://doi.org/10.1214/105051604000000918

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