O presente trabalho consiste em um estudo dos processos fracionários generalizados via sistema de espaço de estados. Essa representação permitirá utilizar um procedimento recursivo para a estimação dos parâmetros desses processos chamado filtro de Kalman. Além disso, apresenta um estudo detalhado sobre o filtro de Kalman, investigando sua utilização na estimação de um processo k-Factor GARMA(p;u; λ; q). Este trabalho verifica que é possível representar um processo k-Factor GARMA(p;u; λ; q) causal por um sistema de espaço de estados, o que possibilita calcular recursivamente a função de verossimilhança exata do processo, por meio do uso do filtro de Kalman, mesmo que a sua representação em espaço de estados tenha dimensão infinita. / This paper presents a study of the generalized fractional processes by using the state space. This representation will allow to use a recursive procedure for the estimation of the parameters of these processes called Kalman filter. In addition, it presents a study with details about the Kalman filter, investigating their use in the estimation of a process k-Factor GARMA(p;u;λ ; q). This work find that is possible to represent a process k-Factor GARMA (p;u;λ ; q) causal in a state space system, which enable to compute recursively the exact likelihood function of the process through the use of the Kalman filter, even though their representation in state space has infinite dimension.

Thesis. 1975. M.S.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / Bibliography: leaves 234-235. / by John G. Lundblad. / M.S.

by John Pui-Fai Sum. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 155-[163]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

The focus of this dissertation is the European Credit Default Swaps (CDSs) market. CDSs are the most popular credit derivative products. Three issues are discussed, the first, which is covered in chapter 2, is the investigation of non-diversifiable jump risk in iTraxx sector indices based on a multivariate model that explicitly admits discrete common jumps for an index and its components. Our empirical research shows that both the iTraxx Non-Financials and their components experience jumps during the sample period, which means that the jump risks in the iTraxx sector index are not diversifiable. The second issue, which is covered in chapter 3 is the component structure of credit default swap spreads and their determinants. We firstly extract a transitory component and a persistent component from two different maturities of the Markit iTraxx index and then regress these components against proxies for several commonly used explanatory variables. Our results show that these explanatory variables have significant but differing impacts on the extracted components, which indicates that a two-factor formulation may be needed to model CDS options. The last issue, which is covered in chapters 4, 5 and 6 is the investigation of the linkage between the credit default swap market and the equity market within the European area. We innovatively calibrate the CDS option with the Heston Model to get the implied volatility in the CDS market, which allows us to investigate both the characteristic of implied volatility in the CDS market and the relationship of the two markets not only on the level of daily changes but also with regard to its second moment. Our analysis shows that the stock market weakly leads the CDS market on daily changes but for implied volatility, the stock market leads the CDS market. A VECM analysis shows that only the stock market contributes to price discovery. For sub-investment grade entities, the interactivities between the implied volatility of the CDS market and the implied volatility of the stock market are stronger, especially during the recent credit crunch period. All these results have important implications for the construction of portfolios with credit-sensitive instruments.

L'apprentissage par renforcement est la réponse du domaine de l'apprentissage numérique au problème du contrôle optimal. Dans ce paradigme, un agent informatique apprend à contrôler un environnement en interagissant avec ce dernier. Il reçoit régulièrement une information locale de la qualité du contrôle effectué sous la forme d'une récompense numérique (ou signal de renforcement), et son objectif est de maximiser une fonction cumulante de ces récompenses sur le long terme, généralement modélisée par une fonction dite de valeur. Le choix des actions appliquées à l'environnement en fonction de sa configuration est appelé une politique, et la fonction de valeur quantifie donc la qualité de cette politique. Ce parangon est très général, et permet de s'intéresser à un grand nombre d'applications, comme la gestion des flux de gaz dans un complexe sidérurgique, que nous abordons dans ce manuscrit. Cependant, sa mise en application pratique peut être difficile. Notamment, lorsque la description de l'environnement à contrôler est trop grande, une représentation exacte de la fonction de valeur (ou de la politique) n'est pas possible. Dans ce cas se pose le problème de la généralisation (ou de l'approximation de fonction de valeur) : il faut d'une part concevoir des algorithmes dont la complexité algorithmique ne soit pas trop grande, et d'autre part être capable d'inférer le comportement à suivre pour une configuration de l'environnement inconnue lorsque des situations proches ont déjà été expérimentées. C'est le problème principal que nous traitons dans ce manuscrit, en proposant une approche inspirée du filtrage de Kalman.

<p>This  report  is  a  part  of  a  master  thesis  project  done  at  Ericsson  Linköping  incooperation with Linköpings Tekniska Högskola (LiTH). This project is divided intwo different parts.  The first part is to create a measurement node that collectsand processes data from network time protocol servers.   It is used to determinethe  quality  of  the  IP  network  at  the  node  and  detect  potential  defects  on  usedtimeservers or nodes on the networks.The second assignment is to analyze the collected data and further improve theexisting synchronization algorithm.  Ip communication is not designed to be timecritical and therefore the NTP protocol needs to be complemented with additionalsignal processing to achieve required accuracy.  Real time requirements limit thecomputational complexity of the signal processing algorithm.</p>

<p>State estimation deals with estimation of the state of an object of interest by observing noisy measurements. The process to obtain the state estimations is called filtering. In this report several filters are compared to an existing one. The new filters deal with nonlinear process and measurement models in a different way than the existing filter. Instead of approximating the nonlinear transformations the probability densities are approximated by a set of points which undergo the nonlinear transformation.</p><p>The application for which the filters will be used is to estimate the position and orientation of a camera in a markerless environment, using data from an inertial measurement unit and a camera. It is found that the corresponding process and measurement models contain nonlinearities and therefore an accuracy improvement is expected with the new filters.</p><p>The new filters are variations of the so-called unscented Kalman filter. Also a discussion on the marginalized particle filter is presented. Instead of using randomly chosen samples as in the particle filter methods, the unscented Kalman filter uses deterministically chosen points. The marginalized particle filter partitions the variables of the system in a linear and a nonlinear part. Linear Kalman filters are applied to the linear variables and a particle filter to the nonlinear variables, thus reducing the computational load. Details of various implementations of the filters are given, as well as the motivation for the specific implementations.</p><p>Tests are carried out to assess the performance of the filters. This is done with both simulation data and real measurements. A comparison is made to the original extended Kalman filter. The tests are focussed on accuracy and computational load.</p><p>Results showed that the use of the new filters did not improve accuracy. This is mainly due to the fact that the nonlinearities are not so severe. Furthermore the filters had a higher computational load, which is an important aspect in the system reviewed in this report. Therefore the current filter need not to be replaced. The unscented Kalman filter is a good alternative to the EKF in case of new applications, since it can handle the system in a black-box manner in contrast to the EKF.</p>

My research is concentrated on applications of linear algebra in engineering, including wavelet analysis and structured matrices and (currently) approximation of large dense matrices by a mosaic of low rank blocks. / Singapore-MIT Alliance (SMA)

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1977. / Also available via the Internet.

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