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Rates of convergence for statistical limit laws in deterministic dynamical systems
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Antoniou, Marios (2018) Rates of convergence for statistical limit laws in deterministic dynamical systems. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3163758~S15
Abstract
We investigate rates of convergence in statistical limit theorems for observables of deterministic dynamical systems and the corresponding questions in homogenization of fast-slow systems. In particular we first use martingale approximations to review the Central Limit Theorem for ergodic stochastic processes under a general framework for expanding maps and retrieve the corresponding rate of convergence to a normal law. We then consider the functional central theorem under a general framework and obtain using a new method the corresponding rate of convergence to a Brownian motion. The main result of the thesis is establishing rates of convergence in homogenization for deterministic maps and multiplicative noise.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Brownian motion processes, Stochastic processes, Martingales (Mathematics), Homogenization (Differential equations), Mappings (Mathematics) | ||||
Official Date: | March 2018 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Melbourne, Ian | ||||
Sponsors: | H2020 European Research Council | ||||
Extent: | v, 107 leaves | ||||
Language: | eng |
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