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Full-Text Articles in Probability
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Doctoral Dissertations
This dissertation is comprised of two separate projects. The first concerns a Markov chain called the Random Logistic Model. For r in (0,4] and x in [0,1] the logistic map fr(x) = rx(1 - x) defines, for positive integer t, the dynamical system xr(t + 1) = f(xr(t)) on [0,1], where xr(1) = x. The interplay between this dynamical system and the Markov chain xr,N(t) defined by perturbing the logistic map by truncated Gaussian noise scaled by N-1/2, where N -> infinity, is studied. A natural question is …