After a review of the notions of Hausdorff and Fourier dimensions from fractal geometry and Fourier analysis and the properties of local times of Brownian motion, we study the Fourier structure of Brownian level sets. We show that if δa(X) is the Dirac measure of one-dimensional Brownian motion X at the level a, that is the measure defined by the Brownian local time La at level a, and μ is its restriction to the random interval [0, L−1 a (1)], then the Fourier transform of μ is such that, with positive probability, for all 0 ≤ β < 1/2, the function u → |u|β|μ(u)|2, (u ∈ R), is bounded. This growth rate is the best possible. Consequently, each Brownian level set, reduced to a compact interval, is with positive probability, a Salem set of dimension 1/2. We also show that the zero set of X reduced to the interval [0, L−1 0 (1)] is, almost surely, a Salem set. Finally, we show that the restriction μ of δ0(X) to the deterministic interval [0, 1] is such that its Fourier transform satisfies E (|ˆμ(u)|2) ≤ C|u|−1/2, u 6= 0 and C > 0. Key words: Hausdorff dimension, Fourier dimension, Salem sets, Brownian motion, local times, level sets, Fourier transform, inverse local times. / Decision Sciences / PhD. (Operations Research)

Summaries in Afrikaans and English / Text in Afrikaans / In hierdie proefskrif word daar gekonsentreer op die bewyslas in die nywerheidshof omdat die nywerheidshof se benadering met betrekking tot die bewyslas verskil van geval tot gevaL afhangende van die aard van die regshulp waarvoor die party je die nywerheidshof nader. In die tweede plek volg 'n bespreking van hoe en deur wie die voorlegging van getuienis aan die nywerheidshof mag geskied, hetsy by wyse van dokumente of getuies en daarbenewens oak 'n bespreking van watter soort getuienis aan die nywerheidshof voorgele mag word met spesifieke verwysing na inter alia, klankopnames, videobande en die resultate van leuenverklikkertoetse. / In this thesis there will be concentrated on the burden of proof in the industrial court because the industrial court's approach in regard to the burden of proof differs from case to case, depending on the nature of the legal aid for which the party /ies approaches the industrial court. In the second place a discussion will follow of how and by whom the presenting of evidence can be done, whether by documents or by witnesses, and in addition thereto also a discussion on which sort of evidence can be presented to the industrial court with specific reference to, inter alia, taperecordings, video tapes and the results of lie-detector tests. / Private Law / LL.M. (Handelsreg)

The objective of this thesis is to provide new insights into determinants of firm access to finance, and the role of the European Central Bank's (ECB) monetary policy. Not only do we describe and analyze the determinants of access to finance, but we focus on the theory of financial intermediation, as well. The key part analyses European Commission (EC)/ECB survey data for 16 euro area economies from 11 survey waves in the period from 2009 to 2014. We build our model using traditional firm-level variables such as firm size and age as well as a novel measure of the ECB's monetary policy stance - the shadow rate. We hypothesize that smaller and younger firms with decreased profitability over the past 6 months and increased leverage over the same period are more likely to report problems with access to finance. Our results are intuitively consistent with theoretical expectations and also show that the looser the monetary policy of the ECB is, the lower the composite financing gap indicator. Interestingly, we do not confirm the existence of risk taking channel of the monetary policy. Overall, we make use of the most recent survey data, extend the dataset, and use modified methodology for our estimation.

This dissertation is cumulative and encompasses three self-contained research articles. These essays share one common theme: the probability that a given stochastic process crosses a certain boundary function, namely the boundary crossing probability, and the related financial and statistical applications. In the first paper, we propose a new Monte Carlo method to price a type of barrier option called the Parisian option by simulating the first and last hitting time of the barrier. This research work aims at filling the gap in the literature on pricing of Parisian options with general curved boundaries while providing accurate results compared to the other Monte Carlo techniques available in the literature. Some numerical examples are presented for illustration. The second paper proposes a Monte Carlo method for analyzing the sensitivity of boundary crossing probabilities of the Brownian motion to small changes of the boundary. Only for few boundaries the sensitivities can be computed in closed form. We propose an efficient Monte Carlo procedure for general boundaries and provide upper bounds for the bias and the simulation error. The third paper focuses on the inverse first-passage-times. The inverse first-passage-time problem deals with finding the boundary given the distribution of hitting times. Instead of a known distribution, we are given a sample of first hitting times and we propose and analyze estimators of the boundary. Firstly, we consider the empirical estimator and prove that it is strongly consistent and derive (an upper bound of) its asymptotic convergence rate. Secondly, we provide a Bayes estimator based on an approximate likelihood function. Monte Carlo experiments suggest that the empirical estimator is simple, computationally manageable and outperforms the alternative procedure considered in this paper.

Este trabalho foi motivado pela necessidade de considerar comportamento estocástico durante o planejamento da produção de sistemas de manufatura, ou seja, o que produzir e em que ordem. Estes sistemas possuem um comportamento estocástico geralmente não considerado no planejamento da produção. O principal objetivo deste trabalho foi obter um método que modelasse sistemas de manufatura e representasse seu comportamento estocástico durante o planejamento de produção destes sistemas. Como os métodos que eram ideais para planejamento não forneciam a modelagem adequada dos sistemas, e os com modelagem adequada não forneciam a capacidade de planejamento necessária, decidiu-se combinar dois métodos para atingir o objetivo desejado. Decidiu-se modelar os sistemas em rede de Petri e convertê-los em processos de decisão markovianos, e então realizar o planejamento com o ultimo. Para que fosse possível modelar as probabilidades envolvidas nos processos, foi proposto um tipo especial de rede de Petri, nomeada rede de Petri fatorada. Utilizando este tipo de rede de Petri, foi desenvolvido o método de conversão em processos de decisão markovianos. A conversão ocorreu com sucesso, conforme testes que mostraram que planos podem ser produzidos utilizando-se algoritmos de ponta para processos de decisão markovianos. / The present work was motivated by the need to consider stochastic behavior when planning the production mix in a manufacturing system. These systems are exposed to stochastic behavior that is usually not considered during production planning. The main goal of this work was to obtain a method to model manufacturing systems and to represent their stochastic behavior when planning the production for these systems. Because the methods that were suitable for planning were not adequate for modeling the systems and vice-versa, two methods were combined to achieve the main goal. It was decided to model the systems in Petri nets and to convert them into Markov decision processes, to do the planning with the latter. In order to represent probabilities in the process, a special type of Petri nets, named Factored Petri nets, were proposed. Using this kind of Petri nets, a conversion method into Markov decision processes was developed. The conversion is successful as tests showed that plans can be produced within seconds using state-of-art algorithms for Markov decision processes.

Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique. En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance. Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya. Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique. Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives. Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées.

In this essay I defend the notion of deductive explanation mainly against two types of putative counterexamples: those found in genuinely indeterministic systems and those found in complex dynamic systems. Using Railton's notions of explanatory information and ideal explanatory text, deductivism is defended in an indeterministic setting. Furthermore, an argument against non-deductivism that hinges on peculiarities of probabilistic causality is presented. The use of the notion of an ideal explanatory text gives rise to problems in accounting for explanations in complex dynamic systems, regardless of whether they are deterministic or not. These problems are considered in the essay and a solution is suggested. This solution forces the deductivist to abandon the requirement that an explanation consists of a deductive argument, but it is argued that the core of deductivism is saved in so far as we, for full explanations, can still adhere to the fundamental requirement: If A explains B, then A is inconsistent with anything inconsistent with B.

Can pay-for-performance increase the motivation of public employees? By providing a basis for personnel decisions, particularly linking rewards to performance, performance appraisals aim to increase employees' work motivation and ultimately to improve their work performance and organizational productivity. With the emphasis on results-oriented management, performance appraisals have become a key managerial tool in the public sector. Critics charge, however, that pay-for-performance is ineffective in the public sector, largely because the link between performance and rewards is weak. However, no one has empirically measured the strength of the linkage. If performance ratings do have an impact on career success in the federal service, they might contribute to race and gender inequality. Although many studies have examined factors affecting gender and racial differences in career success, studies that try to connect gender and racial inequalities to managerial tools are scarce. Using a one percent sample of federal personnel records, the first essay examines the impact of performance ratings on salary increases and promotion probabilities, and the second essay explores whether women and minorities receive lower ratings than comparable white males, and women and minorities receive lower returns on the same level of performance ratings than comparable white males. The first essay finds that performance ratings have only limited impact on salary increases, but that they significantly affect promotion probability. Thus, the argument that performance-rewards link is weak could be partially correct, if it considers only pay-performance relationships. The second essay finds that women receive equal or higher performance ratings than comparable white men, but some minority male groups, particularly black men, tend to receive lower ratings than comparable white men. On the other hand, the returns on outstanding ratings do not differ between women and minority male groups and white men, though women groups seem to have disadvantages in promotion with the same higher ratings as comparable men in highly male-dominant occupations.

From the Proceedings of the 1971 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 22-23, 1971, Tempe, Arizona / Streamflows of monthly or shorter time periods, are, in most parts of the world, conditionally dependent. In studies of planning, commitment and operation decisions concerning reservoirs, it is probably most computationally efficient to use simulation routines for decisions of low dimensions, as planning and commitment, and optimization routines for the highly dimensional operation rule decisions. This presents the major problem of combining the 2 routines, since streamflow dependencies in simulation routines are continuous while the direct stochastic optimization routines are discrete. A stochastic streamflow synthesis routine is described consisting of 2 parts: streamflow probability distribution and dependency analysis and a streamflow generation using the relationships developed. A discrete dependency matrix between streamflow amounts was then sought. Setting as the limits of interest the class 400-500 thousand acre ft in January and 500-600 thousand acre ft in February, and using the transforms specified, the appropriate normal deviates were determined. The next serious problem was calculating the conditional dependency based on the bivariate normal distribution. In order to calculate the joint probability exactly, double integrations would be required and these use too much computer time. For the problem addressed, therefore, the use of 1-dimensional conditional probabilities based on the flow interval midpoint is an adequate and effective procedure.

Emissions from light-duty passenger vehicles represent a significant portion of total criteria pollutant emissions in the United States. Since the 1970s, emissions testing of these vehicles has been required in many major metropolitan areas, including Atlanta, GA, that were designated to be in non-attainment for one or more of the National Ambient Air Quality Standards. While emissions inspections have successfully reduced emissions by identifying and repairing high emitting vehicles, they have been increasingly inefficient as emissions control systems have become more durable and fewer vehicles are in need of repair. Currently, only about 9% of Atlanta area vehicles fail emissions inspection, but every vehicle is inspected annually. This research addresses explores ways to create a more efficient emissions testing program while continuing to use existing testing infrastructure. To achieve this objective, on road vehicle emissions data were collected as a part of the Continuous Atlanta Fleet Evaluation program sponsored the Georgia Department of Natural Resources. These remote sensing data were combined with in-program vehicle inspection data from the Atlanta Vehicle Inspection and Maintenance (I/M) program to establish the degree to which on road vehicle remote sensing could be used to enhance program efficiency. Based on this analysis, a multi-parameter model was developed to predict the probability of a particular vehicle failing an emissions inspection. The parameters found to influence the probability of failure include: vehicle characteristics, ownership history, vehicle usage, previous emission test results, and remote sensing emissions readings. This model was the foundation for a proposed emissions testing program that would create variable timing for vehicle retesting with high and low failure probability vehicles being more and less frequently, respectively, than the current annual cycle. Implementation of this program is estimated to reduce fleet emissions of 17% for carbon monoxide, 11% for hydrocarbons, and 5% for nitrogen oxides in Atlanta. These reductions would be achieved very cost-effectively at an estimated marginal cost of $149, $7,576 and $2,436 per-ton-per-year for carbon monoxide, hydrocarbons, and nitrogen oxides emissions reductions respectfully.