Este trabalho aborda um estudo, a nível introdutório, sobre processos de Markov reversíveis, onde seguimos a exposição de Stroock [24]. Mais especificamente, estudamos cadeias de Markov sobre S (espaço de estados) finito que sejam reversíveis com respeito a uma dada distribuição inicial ¹. Analisamos também a validade do limite limt!1 kPtf ¡ hfi¹ k2;¹ = 0, nos preocupando, principalmente, com a taxa de tal convergência. Por fim, propomos uma Dinâmica de Glauber para o Estado de Gibbs μ(ß) e damos uma cota superior e inferior para a taxa de convergência λß do limite limt!1 kPtf ¡ hfi¹(ß) k2;¹(ß) = 0. Concluindo, apresentamos aplicações, em modelos físicos, da teoria desenvolvida ao longo desta dissertação. / This work approach a study, in introductory level, about reversible Markov processes, where we follow the Stroock´s exposition [24]. More specifically, we study Markov chains about S (space of states) finite that is reversible with respect a initial distribution μ give. Too we analysis the validate of limit limt!1 kPtf ¡ hfi¹ k2;¹ = 0, preoccupying, principally, with the rate of convergence. Finish, we propose a Glauber Dynamics to Gibbs States μ(ß) and we give a lower and upper boundary to rate of convergence λß of the limit limt!1 kPtf ¡ hfi¹(ß) k2;¹(ß) = 0. Concluding, we presents applications, in physical models, of the developed theory in the course these dissertation.

Seguindo o trabalho de S. Gudder, fazemos uma construção de cadeias de Markov quânticas a partir de matrizes complexas, unitárias, estocásticas e analisamos o conceito de interferência nesse contexto, dando atenção para uma cadeia que chamamos de moeda quântica. Estamos interessados na entropia de cadeias de Markov reais, no princípio variacional para energia livre associado e em uma possível construção análoga no caso complexo. Este trabalho visa também dar uma introdução matematicamente rigorosa de certos aspectos de mecânica quântica

Seguindo o trabalho de S. Gudder, fazemos uma construção de cadeias de Markov quânticas a partir de matrizes complexas, unitárias, estocásticas e analisamos o conceito de interferência nesse contexto, dando atenção para uma cadeia que chamamos de moeda quântica. Estamos interessados na entropia de cadeias de Markov reais, no princípio variacional para energia livre associado e em uma possível construção análoga no caso complexo. Este trabalho visa também dar uma introdução matematicamente rigorosa de certos aspectos de mecânica quântica

Este trabalho aborda um estudo, a nível introdutório, sobre processos de Markov reversíveis, onde seguimos a exposição de Stroock [24]. Mais especificamente, estudamos cadeias de Markov sobre S (espaço de estados) finito que sejam reversíveis com respeito a uma dada distribuição inicial ¹. Analisamos também a validade do limite limt!1 kPtf ¡ hfi¹ k2;¹ = 0, nos preocupando, principalmente, com a taxa de tal convergência. Por fim, propomos uma Dinâmica de Glauber para o Estado de Gibbs μ(ß) e damos uma cota superior e inferior para a taxa de convergência λß do limite limt!1 kPtf ¡ hfi¹(ß) k2;¹(ß) = 0. Concluindo, apresentamos aplicações, em modelos físicos, da teoria desenvolvida ao longo desta dissertação. / This work approach a study, in introductory level, about reversible Markov processes, where we follow the Stroock´s exposition [24]. More specifically, we study Markov chains about S (space of states) finite that is reversible with respect a initial distribution μ give. Too we analysis the validate of limit limt!1 kPtf ¡ hfi¹ k2;¹ = 0, preoccupying, principally, with the rate of convergence. Finish, we propose a Glauber Dynamics to Gibbs States μ(ß) and we give a lower and upper boundary to rate of convergence λß of the limit limt!1 kPtf ¡ hfi¹(ß) k2;¹(ß) = 0. Concluding, we presents applications, in physical models, of the developed theory in the course these dissertation.

Orientador: Nelson Luis Saldanha da Fonseca / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-07-25T09:13:10Z (GMT). No. of bitstreams: 1 Pereira_AndreLuizGarcia_M.pdf: 21855074 bytes, checksum: a7eb9c53e873ac7dd0e51f4aba3f9ad7 (MD5) Previous issue date: 1998 / Resumo: Será apresentado neste trabalho uma coletânea de técnicas e teorias úteis para o desenvolvimento de simuladores capazes de representar tráfegos de redes multimídia. Além de um estudo detalhado destas técnicas, foi desenvolvido uma biblioteca de rotinas voltada para a geração de tráfegos e para a simulação de eventos raros. / Abstract: In this dissertation a collection of useful techniques and theories for the development of simulators capable of handling network multimedia traffic. Besides a detail study of this techniques, a library of routines was develop in order to generate traffic and to simulate rare events in networks. / Mestrado / Mestre em Ciência da Computação

M. Ing. (Electrical and Electronic Engineering) / This thesis investigates various methods of modeling fading communication channels. These modeling methods include various techniques for the modeling of different fading mechanisms. The fading mechanism mainly considered throughout this thesis, is slow Rayleigh fading. Concise mathematical methods of modeling the effect that a fading communication channel has on binary digital data passing through it, is considered. A discussion on binary channel models, presented in the past, such as the Gilbert, Gilbert - Elliott and Fritchman channel models is also presented. All of these mathematical channel modeling techniques, are Markov chain based. Most of the investigations undertaken during the course of this work were based on Fritchman channel models. Results indicating the capabilities as well as the short falls of Fritchman models are presented. The experimental results presented here were obtained using dedicated error recording equipment, designed especially for the purpose of undertaking measurements, which enables one to deduce mathematical channel models. Detail regarding this equipment can be found in one of the two accompanying volumes, volume II. Furthermore, a new approach to channel modeling, based on hidden Markov models, is also presented for the modeling of channels with soft decision outputs. Results proving the accuracy of the proposed soft decision modeling technique, are also presented.

For certain Markov processes, K. Ito has defined the Poisson point process of excursions away from a fixed point. The law of this process is determined by a certain measure, called its Characteristic measure. He gives a list of conditions this measure must obey. I add to these conditions, obtaining necessary and sufficient conditions for a measure to arise in this way. The main technique is to use a 'last exit decomposition' related to those of Getoor and Sharpe. The more general problem of excursions away from a fixed set is treated using the Exit system of B. Maisonneuve. This gives a useful technique for constructing new Markov processes from old ones. For example, we obtain a rigorous construction of the Skew Brownian motion of Ito and McKean, and another proof of results of Pittenger and Knight on excision of excursions. A related question is that of determining whether an entrance point for a Markov process remains an entrance point for an h-transform of that process. Let E be an open subset of Euclidean space, with a Green function, and let X be harmonic measure on the Martin boundary Δ of E. I show that, except for a λMλ -null-set of (x,y)εΔ², x is an entrance point for Brownian motion conditioned to leave E at y. R.S. Martin gave examples in dimension 3 or higher, for which there exist minimal accessible Martin boundary points x≠y for which this condition fails. I give a similar example in dimension 2. The argument uses recent results of M. Cranston and T. McConnell, together with Schwarz-Christoffel transformations. / Science, Faculty of / Mathematics, Department of / Graduate

Clustering time-series data into discrete groups can improve prediction as well as providing insight into the nature of underlying, unobservable states of the system. However, temporal heterogeneity and autocorrelation (persistence) in group occupancy can obscure such signals. We use latent-state and hidden Markov models (HMMs), two standard clustering techniques, to model high-resolution hourly movement data from Florida panthers. Allowing for temporal heterogeneity in transition probabilities, a straightforward but rarely explored model extension, resolves previous HMM modeling issues and clarifies the behavioural patterns of panthers. / Thesis / Master of Science (MSc)

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