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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 …
Advanced Sequential Monte Carlo Methods And Their Applications To Sparse Sensor Network For Detection And Estimation, Kai Kang
Doctoral Dissertations
The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this …