Vanishing viscosity limits in the small noise regime for Burgers turbulence
Perfect simulation for birth-and-death processes with applications to RJMCMC
Full text | |
Author(s): |
Lucas Moreira
Total Authors: 1
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Document type: | Doctoral Thesis |
Press: | Campinas, SP. |
Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
Defense date: | 2012-02-16 |
Examining board members: |
Nancy Lopes Garcia;
Jesus Enrique Garcia;
Alexsandro Giacomo Grimbert Gallo;
Florencia Graciela Leonardi;
Miguel Natálio Abadi
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Advisor: | Nancy Lopes Garcia |
Abstract | |
Inspired by Collet, Galves and Leonardi (2008), the original motivation of this paper is to answer the following question: Is it possible to recover the context tree of a length variable chain range through a disturbed sample of chain? Initially consider binary chains of infinite order in which one of the symbols can be modified with a small and fixed probability. We prove that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain if the probability of contamination is small enough. Through this result, we were able to answer affirmatively to the initial question of this work, i.e., it is possible to recover the context tree of the original process using a sample contaminates the estimation procedure. With this, we show that the estimator of the context tree used is robust. Next, consider the following model: given two length variable chains, taking values in the same finite alphabet, at each instant of time, the new process randomly chooses one of the two processes with a large and fixed probability. The chain obtained with greater probability can be seen as a stochastic disturbance of the original chain. For this model, we obtained similar results to the those obtained for the initial model (AU) | |
FAPESP's process: | 08/10693-5 - Inference for long range stochastic processes |
Grantee: | Lucas Moreira |
Support Opportunities: | Scholarships in Brazil - Doctorate |