Este trabalho trata de filtragem robusta para sistemas lineares sujeitos a saltos Markovianos discretos no tempo. Serão desenvolvidas estimativas preditoras e filtradas baseadas em algoritmos recursivos que são úteis para aplicações em tempo real. Serão desenvolvidas duas classes de filtros robustos, uma baseada em uma estratégia do tipo H \'INFINITO\' e a outra baseada no método dos mínimos quadrados regularizados robustos. Além disso, serão desenvolvidos filtros na forma de informação e seus respectivos algoritmos array para estimar esse tipo de sistema. Neste trabalho assume-se que os parâmetros de saltos do sistema Markoviano não são acessíveis. / This work deals with the problem of robust state estimation for discrete-time uncertain linear systems subject to Markovian jumps. Predicted and filtered estimates are developed based on recursive algorithms which are useful in on-line applications. We develop two classes of filters, the first one is based on a H \'INFINITO\' approach and the second one is based on a robust regularized leastsquare method. Moreover, we develop information filter and their respective array algorithms to estimate this kind of system. We assume that the jump parameters of the Markovian system are not acessible.

本文主要目的，在建立一個現金限制(CIA)的兩部門貨幣成長模型。在模 型裡，不同財貨間的邊際技術的轉換率是內生決定的。完全預期的通貨膨 脹會改變財貨間的相對價格，因其受制於現金限制式不同，因此通貨膨脹 經由此管道，在不同的兩部門生產要素移轉的投入，會致使資本累積改變 。

This dissertation presents a low-power high-resolution delta-sigma ADC. Two new architectural design techniques are proposed to reduce the power dissipation of the ADC. Compared to the conventional active adder, the direct charge transfer (DCT) adder greatly saves power by keeping the feedback factor of the active adder unity. However, the inherent delay originated from the DCT adder will cause instability to the modulator and complex additional branches are usually needed to stabilize the loop. A simple and power-efficient technique is proposed to absorb the delay from the DCT adder and the instability issue is therefore solved. Another proposed low-power design technique is to feed differentiated inverted quantization noise to the input of the last integrator. The modulator noise-shaping order with this proposed technique is effectively increased from two to three without adding additional active elements. The delta-sigma ADC with the proposed architectural design techniques has been implemented in transistor-level and fabricated in 0.18 µm CMOS technology. Measurement results showed a SNDR of 99.3 dB, a DR of 101.3 dB and a SFDR of 112 dB over 20 kHz signal bandwidth, resulting in a very low figure-of-merit (FoM) in its application category. Finally, two new circuit ideas, low-power parasitic-insensitive switched-capacitor integrator for delta-sigma ADCs and switched-resistor tuning technique for highly linear Gm-C filter design are presented. / Graduation date: 2012 / Access restricted to the OSU Community at author's request from June 9, 2012 - June 9, 2014

This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are: I. Å. Brännström, Single species population models from first principles. II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models. III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology. IV. Å. Brännström, An area integral estimate for higher order parabolic equations. In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter & Broomhead (2001) and Johansson & Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals. The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds. In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal. Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.

本財務預警模型研究延續Shumway(2001)年所提出的離散型風險模型(Discrete-time Hazard Model)架構，即Shumway 所稱之多期邏輯斯迴歸模型(Multiperiod logistic regression model) ，來建立銀行財務預警模型。不同於Shumway所提出的Log 基期風險式，研究者根據實際財務危機發生機率圖提出Quadratic 基期風險式。由於離散型風險模型考量與時間相依共變量(Time-dependent covariate)，該模型可以納入隨時間變動的的市場與總體變數，這是單期模型無法達到的。實證結果顯示，不論是否有加入總體與市場變數，Quadratic 基期風險式離散型模型在樣本內檢測表現都比單期模型與Log 基期風險式離散型模型好，研究亦顯示樣本外的預測Quadratic基期風險式在大多數情況都優於Log 基期風險式與單期模型 / This paper continues Shumway(2001) studies on discrete time hazard model, the so called multi-period logistic regression model, to develop a bank failure early warning model . Different from log baseline hazard form proposed by Shumway, author present quadratic baseline hazard form based on the pattern of real default rate. By incorporating time-varying covariates, our model enables us to utilize macroeconomic and market variables, which cannot be incorporated into in a one-period model. We find that our model significantly outperforms the single period logit model and Log baseline hazard model with and without the macroeconomic and market variables at in-sample estimation. The improvement in accuracy comes both from the time-series bank-specific variables and from the time-series macroeconomic variables. Our research also shows that quadratic baseline hazard model outperforms Log baseline hazard model and single period logit model in out-of-sample prediction.

A repetitive control method for output voltage control of a three phase uninterruptible power supply (UPS) with isolation transformer is investigated. In the method voltage control loop is employed in the stationary dq frame. The controller eliminates the periodic errors on the output voltages due to inverter voltage nonlinearity and load disturbances. The controller design and implementation details are given. The controller is implemented on a 5-kVA UPS prototype which is constructed in laboratory. Linear and nonlinear loads for balanced and unbalanced load operating conditions are considered. The steady-state and dynamic performance of the control method are investigated in detail. The theory of the control strategy is verified by means of simulations and experiments.

The parallel active filter (PAF) is the modern solution for harmonic current mitigation and reactive power compensation of nonlinear loads. This thesis is dedicated to detailed analysis, design, control, and implementation of a PAF for a 3- phase 3-wire rectifier load. Specifically, the current regulator and switching ripple filter (SRF) are thoroughly investigated. A novel discrete time hysteresis current regulator with multi-rate current sampling and flexible PWM output, DHCR3, is proposed. DHCR3 exhibits a high bandwidth while limiting the maximum switching frequency for thermal stability and its implementation is simple. In addition to the development of DHCR3, in the thesis state of the art current regulation methods are considered and thoroughly compared with DHCR3. Since the current regulator type determines the SRF topology choice, various SRF topologies are considered and a thorough design study is conducted and SRF topology selection and parameter determination methods are presented via numerical examples. Through a PAF designed for a 10kW diode/thyristor rectifier load, the superior performance of DHCR3 is verified through simulations and experiments and via comparison to other current regulators. The sufficient switching ripple attenuation of the SRF structures for the designed PAF system and the overall performance of the designed and built PAF system are demonstrated via detailed computer simulations and laboratory experiments. This thesis aids the PAF current regulator and SRF selection, design, and implementation.

Series Active Filters (SAF) are designed for harmonic isolation and load voltage regulation of single-phase and three-phase voltage harmonic source type nonlinear loads. The novel Absolute Value Method (AVM) for load voltage harmonic extraction is proposed and applied in the control algorithm of SAF. The SAF compensated systems are represented by simplified linear models such that SAF controller gains can be easily determined. Harmonic isolation and load voltage regulation performances of 2.5 kW single-phase and 10 kW three-phase SAF compensated systems are evaluated by detailed simulations. Laboratory prototype single-phase and three-phase SAFs and loads are designed and manufactured. Digital signal processor based control platform is employed. Exclusive laboratory tests are conducted. Via laboratory experiments and simulations it is shown that AVM yields superior harmonic isolation and load voltage regulation performance compared to the conventional low/high pass filtering method. Theory, simulations, and experiments are well correlated and illustrate the feasibility of the proposed method.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgage origination, data as well as bank bailouts. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the sequel, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of SORs' capital, information, ratings, risk and valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete-time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.

Many analysts believe that problems in the United States housing market initiated the 2007-2009 global financial crisis. In this regard, the subprime mortgage crisis (SMC) shook the foundations of the financial industry by causing the failure of many iconic Wall Street investment banks and prominent depository institutions. This crisis stymied credit extension to households and businesses thus creating credit crunches and, ultimately, a global recession. This thesis specifically discusses the SMC and its components, causes, consequences and cures in relation to subprime mortgage origination, data as well as bank bailouts. In particular, the SMC has highlighted the fact that risk, credit ratings, profit and valuation as well as capital regulation are important banking considerations. With regard to risk, the thesis discusses credit (including counterparty), market (including interest rate, basis, prepayment, liquidity and price), tranching (including maturity mismatch and synthetic), operational (including house appraisal, valuation and compensation) and systemic (including maturity transformation) risks. The thesis introduces the IDIOM hypothesis that postulates that the SMC was largely caused by the intricacy and design of subprime agents, mortgage origination that led to information problems (loss, asymmetry and contagion), valuation opaqueness and ineffective risk mitigation. It also contains appropriate examples, discussions, timelines as well as appendices about the main results on the aforementioned topics. Numerous references point to the material not covered in the thesis, and indicate some avenues for further research. In the sequel, the banks that we study are subprime interbank lenders (SILs), subprime originators (SORs), subprime dealer banks (SDBs) and their special purpose vehicles (SPVs) such as Wall Street investment banks and their special structures as well as subprime investing banks (SIBs). Furthermore, the primary subprime agents that we consider are house appraisers (HAs), mortgage brokers (MBs), mortgagors (MRs), servicers (SRs), trustees, underwriters and credit enhancement providers (CEPs). Also, the insurers involved in the subprime market are originator mortgage insurers (OMIs) and monoline insurers (MLIs). The main components of the SMC are MRs, the housing market, SDBs/hedge funds/money market funds/SIBs, the economy as well as the government (G) and central banks. Here, G either plays a regulatory, bailout or policymaking role. Most of the aforementioned banks and agents are assumed to be risk neutral with SOR being the exception since it can be risk (and regret) averse on occasion. The three main aspects of the SMC - subprime mortgage origination, data and bailouts - that we cover in this thesis and the chapters in which they are found are outlined below. In Chapter 2, we discuss the dynamics of SORs' capital, information, ratings, risk and valuation under mortgage origination. In particular, we model subprime mortgages that are able to fully amortize, voluntarily prepay or default and construct a discrete-time model for SOR risk and profit incorporating costs of funds and mortgage insurance as well as loan losses. Furthermore, a constrained optimal valuation problem for SORs under mortgage origination is solved. In addition, we show how high loan-to-value ratios curtailed the refinancing of subprime mortgages, while low ratios imply favorable house equity for subprime MRs. Chapter 2 also explores the relationship between Basel capital regulation and the SMC. This involves studying bank credit and capital under Basel regulation. Further issues dealt with are the quantity and pricing of subprime mortgages as well as credit ratings under Basel capital regulation. A key problem is whether Basel capital regulation exacerbated the SMC. Very importantly, the thesis answers this question in the affirmative. Chapter 3 contains subprime data not presented in Chapters 2. We present other mortgage data that also have connections with the main subprime issues raised. In Chapter 4, a troubled SOR's recapitalization by G via subprime bank bailouts is discussed. Our research supports the view that if SOR is about to fail, it will have an incentive not to extend low risk mortgages but rather high risk mortgages thus shifting risk onto its creditors. Here, for instance, we analyze the efficiency of purchasing toxic structured mortgage products from troubled SORs as opposed to buying preferred and common equity. In this regard, we compare the cases where SORs' on-balance sheet mortgages are fully amortizing, voluntarily prepaying (refinancing and equity extraction) and involuntarily prepaying (defaulting). If bailing out SORs considered to be too big to fail involves buying assets at above fair market values, then these SORs are encouraged ex-ante to invest in high risk mortgages and toxic structured mortgage products. Contrary to the policy employed by G, purchasing common (preferred) equity is always the most (least) ex-anteand ex-post-efficient type of capital injection. Our research confirms that this is true irrespective of whether SOR volunteers for recapitalization or not. In order to understand the key results in Chapters 2 to 4, a working knowledge of discrete-time stochastic modeling and optimization is required. The work presented in this thesis is based on a book (see [103]), 2 peer-reviewed international journal articles (see [51] and [105]), 2 peer-reviewed chapters in books (see [104] and [110]) and 4 peer-reviewed conference proceedings paper (see [23], [106], [107] and [109]). / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2011.