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Deterministic approximation schemes with computable errors for the distributions of Markov chains

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Title: Deterministic approximation schemes with computable errors for the distributions of Markov chains
Authors: Kuntz Nussio, Juan
Item Type: Thesis or dissertation
Abstract: This thesis is a monograph on Markov chains and deterministic approximation schemes that enable the quantitative analysis thereof. We present schemes that yield approximations of the time-varying law of a Markov chain, of its stationary distributions, and of the exit distributions and occupation measures associated with its exit times. In practice, our schemes reduce to solving systems of linear ordinary differential equations, linear programs, and semidefinite pro- grams. We focus on the theoretical aspects of these schemes, proving convergence and providing computable error bounds for most of them. To a lesser extent, we study their practical use, applying them to a variety of examples and discussing the numerical issues that arise in their implementation.
Content Version: Open Access
Issue Date: Oct-2017
Date Awarded: Apr-2018
URI: http://hdl.handle.net/10044/1/59103
DOI: https://doi.org/10.25560/59103
Supervisor: Stan, Guy-Bart
Barahona, Mauricio
Sponsor/Funder: Biotechnology and Biological Sciences Research Council (Great Britain)
Funder's Grant Number: BB/F017510/1
Department: Bioengineering
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Bioengineering PhD theses



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