The Annals of Applied Probability

Stability in distribution of randomly perturbed quadratic maps as Markov processes

Rabi Bhattacharya and Mukul Majumdar

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Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1n+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.

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Ann. Appl. Probab., Volume 14, Number 4 (2004), 1802-1809.

First available in Project Euclid: 5 November 2004

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40] 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]

Quadratic maps Markov process invariant probability


Bhattacharya, Rabi; Majumdar, Mukul. Stability in distribution of randomly perturbed quadratic maps as Markov processes. Ann. Appl. Probab. 14 (2004), no. 4, 1802--1809. doi:10.1214/105051604000000918.

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