Stability in Distribution of Randomly Perturbed Quadratic Maps as Markov Processes

Rabi Bhattacharya and Mukul Majumdar
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Rabi Bhattacharya: Indiana U
Mukul Majumdar: Cornell U

Working Papers from Cornell University, Center for Analytic Economics

Abstract: Iteration of randomly chosen quadtratic maps defines a Markov process: X[subscript n + 1] = epsilon[subscript n + 1] X[subscript n](1 - X[subscript n]), where epsilon[subscript n] are i.i.d. with values in the parameter space [0, 4] of quadratic maps F[subscript theta](x) = theta*x(1 - x). Its study is of significance not only as an important Markov model, but also for dynamical systems defined by the individual quadratic maps themselves. In this article a broad criterion is established for positive Harris recurrence of X[subscript n], whose invariant probability may be viewed as an approximation to the so-called Kolmogorov measure of a dynamical system.

Date: 2002-05
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Persistent link: https://EconPapers.repec.org/RePEc:ecl:corcae:02-03

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