Cadeias de Markov clássicas e quânticas

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

Analysis of contagion from the constant conditional correlation model with Markov regime switching

Over the last decades, the analysis of the transmissions of international nancial events has become the subject of many academic studies focused on multivariate volatility models volatility. The goal of this study is to evaluate the nancial contagion between stock market returns. The econometric approach employed was originally presented by Pelletier (2006), named Regime Switching Dynamic Correlation (RSDC). This methodology involves the combination of Constant Conditional Correlation Model (CCC) proposed by Bollerslev (1990) with Markov Regime Switching Model suggested by Hamilton and Susmel (1994). A modi cation was made in the original RSDC model, the introduction of the GJR-GARCH model formulated in Glosten, Jagannathan e Runkle (1993), on the equation of the conditional univariate variances to allow asymmetric e ects in volatility be captured. The database was built with the series of daily closing stock market indices in the United States (SP500), United Kingdom (FTSE100), Brazil (IBOVESPA) and South Korea (KOSPI) for the period from 02/01/2003 to 09/20/2012. Throughout the work the methodology was compared with others most widespread in the literature, and the model RSDC with two regimes was de ned as the most appropriate for the selected sample. The set of results provide evidence for the existence of nancial contagion between markets of the four countries considering the de nition of nancial contagion from the World Bank called very restrictive. Such a conclusion should be evaluated carefully considering the wide diversity of de nitions of contagion in the literature.

Mudanças de regimes na função de reação do Banco Central do Brasil : uma abordagem utilizando Markov Regime Switching

O presente trabalho busca identificar a ocorrência, duração e probabilidades de transição de diferentes regimes na condução da política monetária no Brasil a partir da implantação do sistema de metas de inflação em 1999. A estimação da função de reação do Banco Central do Brasil é realizada a partir de uma Regra de Taylor forward looking para uma economia aberta, onde utilizamos a metodologia Markov Regime Switching para caracterizar de forma endógena os diferentes regimes de política monetária. Os resultados obtidos indicam a ocorrência de três regimes distintos de política monetária a partir da implantação do sistema de metas de inflação no Brasil. O primeiro regime ocorre durante 21% do período estudado e se caracteriza pela não aderência ao princípio de Taylor e discricionariedade da autoridade monetária, que reage demonstrando maior sensibilidade ao hiato do produto. O segundo regime é o de maior duração, ocorre durante 67% do período estudado, e se caracteriza pela aderência ao princípio de Taylor e equilíbrio nos pesos atribuídos pelo Banco Central tanto ao hiato do produto como ao desvio das expectativas de inflação com relação à meta. Já o terceiro regime ocorre durante 12% do período estudado e se caracteriza não somente pela aderência ao princípio de Taylor, como também por uma maior aversão ao desvio das expectativas de inflação com relação à meta.

Algoritmos genéticos: uso de lógica nebulosa e análise de convergência por cadeia de Markov

In this work, the Markov chain will be the tool used in the modeling and analysis of convergence of the genetic algorithm, both the standard version as for the other versions that allows the genetic algorithm. In addition, we intend to compare the performance of the standard version with the fuzzy version, believing that this version gives the genetic algorithm a great ability to find a global optimum, own the global optimization algorithms. The choice of this algorithm is due to the fact that it has become, over the past thirty yares, one of the more importan tool used to find a solution of de optimization problem. This choice is due to its effectiveness in finding a good quality solution to the problem, considering that the knowledge of a good quality solution becomes acceptable given that there may not be another algorithm able to get the optimal solution for many of these problems. However, this algorithm can be set, taking into account, that it is not only dependent on how the problem is represented as but also some of the operators are defined, to the standard version of this, when the parameters are kept fixed, to their versions with variables parameters. Therefore to achieve good performance with the aforementioned algorithm is necessary that it has an adequate criterion in the choice of its parameters, especially the rate of mutation and crossover rate or even the size of the population. It is important to remember that those implementations in which parameters are kept fixed throughout the execution, the modeling algorithm by Markov chain results in a homogeneous chain and when it allows the variation of parameters during the execution, the Markov chain that models becomes be non - homogeneous. Therefore, in an attempt to improve the algorithm performance, few studies have tried to make the setting of the parameters through strategies that capture the intrinsic characteristics of the problem. These characteristics are extracted from the present state of execution, in order to identify and preserve a pattern related to a solution of good quality and at the same time that standard discarding of low quality. Strategies for feature extraction can either use precise techniques as fuzzy techniques, in the latter case being made through a fuzzy controller. A Markov chain is used for modeling and convergence analysis of the algorithm, both in its standard version as for the other. In order to evaluate the performance of a non-homogeneous algorithm tests will be applied to compare the standard fuzzy algorithm with the genetic algorithm, and the rate of change adjusted by a fuzzy controller. To do so, pick up optimization problems whose number of solutions varies exponentially with the number of variables

Modelagem de usinas eólicas através de um processo de Markov e técnicas de confiabilidade para a estimativa anual da energia produzida

This study aims to use a computational model that considers the statistical characteristics of the wind and the reliability characteristics of a wind turbine, such as failure rates and repair, representing the wind farm by a Markov process to determine the estimated annual energy generated, and compare it with a real case. This model can also be used in reliability studies, and provides some performance indicators that will help in analyzing the feasibility of setting up a wind farm, once the power curve is known and the availability of wind speed measurements. To validate this model, simulations were done using the database of the wind farm of Macau PETROBRAS. The results were very close to the real, thereby confirming that the model successfully reproduced the behavior of all components involved. Finally, a comparison was made of the results presented by this model, with the result of estimated annual energy considering the modeling of the distribution wind by a statistical distribution of Weibull

Extraction of Building Roof Contours From LiDAR Data Using a Markov-Random-Field-Based Approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Extração automática de contornos de telhados usando dados de varredura a laser e campos randômicos de Markov

This paper proposes a methodology for automatic extraction of building roof contours from a Digital Elevation Model (DEM), which is generated through the regularization of an available laser point cloud. The methodology is based on two steps. First, in order to detect high objects (buildings, trees etc.), the DEM is segmented through a recursive splitting technique and a Bayesian merging technique. The recursive splitting technique uses the quadtree structure for subdividing the DEM into homogeneous regions. In order to minimize the fragmentation, which is commonly observed in the results of the recursive splitting segmentation, a region merging technique based on the Bayesian framework is applied to the previously segmented data. The high object polygons are extracted by using vectorization and polygonization techniques. Second, the building roof contours are identified among all high objects extracted previously. Taking into account some roof properties and some feature measurements (e. g., area, rectangularity, and angles between principal axes of the roofs), an energy function was developed based on the Markov Random Field (MRF) model. The solution of this function is a polygon set corresponding to building roof contours and is found by using a minimization technique, like the Simulated Annealing (SA) algorithm. Experiments carried out with laser scanning DEM's showed that the methodology works properly, as it delivered roof contours with approximately 90% shape accuracy and no false positive was verified.

Variable parameter and double sampling (X)over-bar charts in the presence of correlation: The Markov chain approach

The general assumption under which the (X) over bar chart is designed is that the process mean has a constant in-control value. However, there are situations in which the process mean wanders. When it wanders according to a first-order autoregressive (AR (1)) model, a complex approach involving Markov chains and integral equation methods is used to evaluate the properties of the (X) over bar chart. In this paper, we propose the use of a pure Markov chain approach to study the performance of the (X) over bar chart. The performance of the chat (X) over bar with variable parameters and the (X) over bar with double sampling are compared. (C) 2011 Elsevier B.V. All rights reserved.

Métodos estatisticos em cadeias de Markov

Este trabalho tem como objetivo o estudo do comportamento assintótico da estatística de Pearson (1900), que é o aparato teórico do conhecido teste qui-quadrado ou teste x2 como também é usualmente denotado. Inicialmente estudamos o comportamento da distribuição da estatística qui-quadrado de Pearson (1900) numa amostra {X1, X2,...,Xn} quando n → ∞ e pi = pi0 , 8n. Em seguida detalhamos os argumentos usados em Billingley (1960), os quais demonstram a convergência em distribuição de uma estatística, semelhante a de Pearson, baseada em uma amostra de uma cadeia de Markov, estacionária, ergódica e com espaço de estados finitos S

Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process

Estimador do Tipo Núcleo para Densidades Limites de Cadeias de Markov com Espaço de Estados Geral

In this work we studied the consistency for a class of kernel estimates of f f (.) in the Markov chains with general state space E C Rd case. This study is divided into two parts: In the first one f (.) is a stationary density of the chain, and in the second one f (x) v (dx) is the limit distribution of a geometrically ergodic chain

Modelagem dos algorítmos simples e Simulated Annealing por cadeias de Markov

Os Algoritmos Genético (AG) e o Simulated Annealing (SA) são algoritmos construídos para encontrar máximo ou mínimo de uma função que representa alguma característica do processo que está sendo modelado. Esses algoritmos possuem mecanismos que os fazem escapar de ótimos locais, entretanto, a evolução desses algoritmos no tempo se dá de forma completamente diferente. O SA no seu processo de busca trabalha com apenas um ponto, gerando a partir deste sempre um nova solução que é testada e que pode ser aceita ou não, já o AG trabalha com um conjunto de pontos, chamado população, da qual gera outra população que sempre é aceita. Em comum com esses dois algoritmos temos que a forma como o próximo ponto ou a próxima população é gerada obedece propriedades estocásticas. Nesse trabalho mostramos que a teoria matemática que descreve a evolução destes algoritmos é a teoria das cadeias de Markov. O AG é descrito por uma cadeia de Markov homogênea enquanto que o SA é descrito por uma cadeia de Markov não-homogênea, por fim serão feitos alguns exemplos computacionais comparando o desempenho desses dois algoritmos

Teoria da Ruína em um Modelo de Markov com dois Estados

In this work, we present a risk theory application in the following scenario: In each period of time we have a change in the capital of the ensurance company and the outcome of a two-state Markov chain stabilishs if the company pays a benece it heat to one of its policyholders or it receives a Hightimes c > 0 paid by someone buying a new policy. At the end we will determine once again by the recursive equation for expectation the time ruin for this company

Estimadores do tipo núcleo para a densidade de transição de uma cadeia de markov com espaço de estados geral

In this work, we studied the strong consistency for a class of estimates for a transition density of a Markov chain with general state space E ⊂ Rd. The strong ergodicity of the estimates for the density transition is obtained from the strong consistency of the kernel estimates for both the marginal density p(:) of the chain and the joint density q(., .). In this work the Markov chain is supposed to be homogeneous, uniformly ergodic and possessing a stationary density p(.,.)