Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

2005/03/24 by Rabi Bhattacharya, Mukul Majumdar
Mathematics · #math.PR #msc:60J05 #msc:60J20 #msc:37H10.

paper · pdf · doi:10.1214/105051604000000918

published as Annals of Applied Probability 2004, Vol. 14, No. 4, 1802-1809 · 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)

arxiv created 2005/03/24 · arxiv updated 2009/12/01

Abstract

Iteration of randomly chosen quadratic maps defines a Markov process: X_n+1=ε_n+1X_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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