>Magister Scientiae - MSc / The study focusses on the transport sector, where company participation level is measured at approximately 20% of levy paying enterprises, and this level is mostly based on relatively high levels of participation from large and medium sized companies. The study explores the relationship between SETAs (sector education training authorities) and the companies within the sectors they are mandated to serve by researching the TETA maritime sub sector. The research focus is on small companies and the focus is specifically on the low rate of participation of smaller entities in the skills development landscape. The consequences of the lack of participation are investigated and the study concludes that the SETAs ability to effectively research its sector skills, as well as the SETAs ability to provide effective skills planning in support of the national agenda, are both negatively affected by current levels of poor participation. The research was conducted on small fishing companies registered with the Transport Education and Training Authority (TETA), in order to determine the reasons for low participation in the government mandatory grant scheme. The research is survey based across participating small companies and non-participating small companies.

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Diese Dissertation untersucht Aspekte des Zusammenspiels von ergodischem Langzeitver- halten und der Glättungseigenschaft dynamischer Systeme, die von stochastischen Differen- tialgleichungen (SDEs) mit Sprüngen erzeugt sind. Im Speziellen werden SDEs getrieben von Lévy-Prozessen und der Marcusschen kanonischen Gleichung untersucht. Ein vari- ationeller Ansatz für den Malliavin-Kalkül liefert eine partielle Integration, sodass eine Variation im Raum in eine Variation im Wahrscheinlichkeitsmaß überführt werden kann. Damit lässt sich die starke Feller-Eigenschaft und die Existenz glatter Dichten der zuge- hörigen Markov-Halbgruppe aus einer nichtstandard Elliptizitätsbedingung an eine Kom- bination aus Gaußscher und Sprung-Kovarianz ableiten. Resultate für Sprungdiffusionen auf Untermannigfaltigkeiten werden aus dem umgebenden Euklidischen Raum hergeleitet. Diese Resultate werden dann auf zufällige dynamische Systeme angewandt, die von lin- earen stochastischen Differentialgleichungen erzeugt sind. Ruelles Integrierbarkeitsbedin- gung entspricht einer Integrierbarkeitsbedingung an das Lévy-Maß und gewährleistet die Gültigkeit von Oseledets multiplikativem Ergodentheorem. Damit folgt die Existenz eines Lyapunov-Spektrums. Schließlich wird der top Lyapunov-Exponent über eine Formel der Art von Furstenberg–Khasminsikii als ein ergodisches Mittel der infinitesimalen Wachs- tumsrate über die Einheitssphäre dargestellt. / The present thesis investigates certain aspects of the interplay between the ergodic long time behavior and the smoothing property of dynamical systems generated by stochastic differential equations (SDEs) with jumps, in particular SDEs driven by Lévy processes and the Marcus’ canonical equation. A variational approach to the Malliavin calculus generates an integration-by-parts formula that allows to transfer spatial variation to variation in the probability measure. The strong Feller property of the associated Markov semigroup and the existence of smooth transition densities are deduced from a non-standard ellipticity condition on a combination of the Gaussian and a jump covariance. Similar results on submanifolds are inferred from the ambient Euclidean space. These results are then applied to random dynamical systems generated by linear stochas- tic differential equations. Ruelle’s integrability condition translates into an integrability condition for the Lévy measure and ensures the validity of the multiplicative ergodic theo- rem (MET) of Oseledets. Hence the exponential growth rate is governed by the Lyapunov spectrum. Finally the top Lyapunov exponent is represented by a formula of Furstenberg– Khasminskii–type as an ergodic average of the infinitesimal growth rate over the unit sphere.

現今各國之稅攻，類皆以推行法人所得稅為要務，期能建立直接稅為主幹的稅制。法 人所得稅的發展，其歷史至今不過六、七十年，但在各國歲入上已占有重要的地位。 因之，對法人所得稅的諸項問題加以研討，似有其必要。 法人所得稅與個人所得稅之並行，各國不乏其例。法人所得在課征法人所得稅之後， 分配於其構成分子時，尚須課征個人所得稅，遂使同一所得被課雙重所得稅，此種情 形是否為重複課稅，不無問題。若其為重複課稅，又應如何補救﹖其補救方法雖甚繁 多，但在實行時則應視經濟環境與需要，以及稅務行政效率如何作為選擇之依據。 對於法人所得稅的性質，一般均認為是直接稅。直接稅是不能轉嫁其稅負於他人的。 然而法人所得稅是否不能轉嫁，則頗有疑問。傳統的理論認為絕對不會轉嫁，但新的 理論及企業界的統計，則認為法人所得稅在相當期間將會轉嫁，祇其轉嫁的程度如何 不易測定而已。 法人所得稅係屬所得稅之一種，是否可以與個人所得稅同樣採用高度的累進稅率，不 無研究餘地。就平均社會財富的觀點來看，法人所得稅採用累進稅率，對平均財富確 具有相當的功效。因為根據固德氏（Richard Goode ）的統計，法人所得確是造成財富集中的一項重要原因，尤其在經濟發達的國家更是 如此。但就鼓勵儲蓄，增加投資的觀點來說，因為累進稅足以妨害儲蓄、減低投資的 誘因，對於經濟發展發生不利的影響，所以法人所稅之採用累進稅率很不適宜。另就 各國法人所得稅稅的演變來看，法人所得稅的稅率亦有趨於比例稅的傾向。此乃經濟 政策重於社會政策的應有措施。 本稿在研究以上三個理論問題以後，再提出兩個技術性的問題。一為固定資產的折舊 問題；一為存貨估價的問題。前者是固定資產估價的主要問題，後者是流動資產評價 的重要項目。折舊的高低、存貨的多寡，對法人所得稅都有直接性的影響。本稿對折 舊及存貨皂的計算，就各種可能採用的方法加以討論，以明其對法人所得稅究有如何 的影響。

L’évolution économique et sociale comparée de deux régions sénégalaise dans le processus de décolonisation : Le Boundou et le Gadiaga 1885-1980Ce travail est le diagnostic de l’évolution interne du Boundou et du Gadiaga (Sénégal oriental) dont les économies respectives n’ont suscité que peu d’intérêt pour le pouvoir colonial et les élites postcoloniales. Le processus et les mécanismes de leur marginalisation sont jusqu’ici mollement signalés pour ce qui concerne le Gadiaga et ne sont pas envisagés dans le cas du Boundou ; d’ailleurs, les travaux antérieurs sont exclusivement circonscrits dans la période de la domination coloniale, et n’établissent aucune "passerelle" entre les manifestations coloniales et postcoloniales de la marginalisation.Cette exclusion de l’économie globale du Sénégal en toute époque est la résultante de l’orientation des politiques économiques et de la faible opportunité offertes par les politiques publiques à certaines régions. Les facteurs de la marginalisation du Boundou et du Gadiaga sont pour ainsi dire d’ordre structurels (absence d’investissement digne de ce nom et de solutions économiques durables) et non conjoncturels. Sur le plan social, les conséquences économiques sont lourdement ressenties, avec la genèse de phénomènes tels l’exode rural, l’émigration massive et organisée de travail et le bouleversement des structures sociales, ce qui accentue à rebours le retard économique. Il se produit à terme une sorte de cercle vicieux de la marginalisation puisque l’accentuation du retard économique par les phénomènes sociaux, encourage les autorités publiques à différer les investissements, voire à y renoncer, en prenant parfois pour seul prétexte la régression démographique dont sont victimes toutes les "périphéries".La similarité de la situation économique entre le « temps partagé » colonial et le « temps propre » postcolonial et les comportements sociaux considérés comme leurs effets induits ne permettent-elle pas de dire que le schéma de gestion de l’État moderne du Sénégal est simplement le rejeton de la politique coloniale. / The economic and social evolution compared by two regions of Senegal in the process of decolonisation: Boundou and Gadiaga on 1885-1980This thesis is the analysis of the internal evolution of Boundou and Gadiaga (Eastern Senegal) whose economies have been little entitled to the colonial and postcolonial elites. The processes and mechanisms of marginalisation are so far softly reported regarding the Gadiaga’s area but this has not been considered in the case of Boundou, and indeed previous work exclusively restricted to the period of colonial domination and makes no “link” between the colonial and postcolonial manifestations of marginalisation.This exclusion of the overall economy of Senegal in many ways and any time is the result of the orientation of economic policies and low opportunities offered by public policies in certain areas. The factors of marginalisation of Boundou Gadiaga are basically structural order (lack of substantial investment and lack of vision and strategy on long run but weakness of sustainable economic approaches) and non-cyclical economic mechanism. Along the social aspects, the population undergoes heavily the economic consequences of the lackluster of the region, and the conditions entail the mass movement of population from rural to urban area (rural exodus) and the disruption of social structures, which increase the pressure of the economic on backwardness. It occurs on short run vicious circle of marginalisation since the accentuation of economic backwardness by social phenomena, encourages public authorities to push back investment’s programs or cancel it, by spotlighting the pretext of the declining population.The similarity of the economic condition between the “shared time” colonial and “owned time” postcolonial and the social behaviours considered induced effects does not allow the scheme management of the modern state of Senegal is simply the offshoot of colonial policy.

Copyright is conventionally justified as an incentive to produce and disseminate works of authorship. We can justify and theorise copyright more richly, not least because empirical evidence does not support the incentive narrative. Rather than focussing on quantitative matters such as the number of works incentivised and produced, we should consider copyright's qualitative influence on culture. A threshold objection to such an approach is the risk of cultural paternalism. This objection can be overcome. Rather than specifying paternalistic standards of merit for works, we can target the conditions under which their creation and consumption takes place. I argue, firstly, that we should adopt the following high-level principles: (i) that the conditions of creation and consumption of works should be conducive to democratic deliberation (democracy) and (ii) that they should facilitate the development of human capabilities (autonomy). Secondly, I propose that we pursue three mid-level objectives, which are helpful indicia of democracy and autonomy: - a fair and wide distribution of communicative and cultural power (inclusiveness); - diversity in the content and perspectives available to the public (diversity); and - conditions that permit authors and users of works to engage rigorously with the conventions of the media in which they operate (rigour). It is often said that copyright obstructs important qualitative objectives, like freedom of expression, and that we could better pursue these goals by weakening copyright and relying on non-proprietary alternatives. My approach produces a more optimistic, but also more complicated, view of copyright. While copyright's qualitative influence is not optimal, reductions in the strength and scope of copyright sometimes produces conditions and incentive structures that are worse for inclusiveness, diversity and rigour than stronger copyright. For example, both attention and wealth are highly concentrated in networked information economies driven by free sharing of content, and this is bad for diversity or inclusiveness. Online business models, based on surveillance of users' consumption of free works, are corrosive of autonomy and democracy. Merely removing copyright-based restrictions on the sharing of works is not a panacea for copyright's ills. A qualitative theory such as mine equips us to better understand and calibrate more richly the trade-offs involved in copyright policy decisions, and encourages us to treat copyright as part of a broader, qualitatively-oriented information and cultural policy.

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Ce travail de thèse porte sur différentes caractérisations des modèles multivariés de stables-Tweedie multiples dans le cadre des familles exponentielles naturelles sous la propriété de "steepness". Ces modèles parus en 2014 dans la littérature ont été d’abord introduits et décrits sous une forme restreinte des stables-Tweedie normaux avant les extensions aux cas multiples. Ils sont composés d’un mélange d’une loi unidimensionnelle stable-Tweedie de variable réelle positive fixée, et des lois stables-Tweedie de variables réelles indépendantes conditionnées par la première fixée, de même variance égale à la valeur de la variable fixée. Les modèles stables-Tweedie normaux correspondants sont ceux du mélange d’une loi unidimensionnelle stable-Tweedie positive fixé et les autres toutes gaussiennes indépendantes. A travers des cas particuliers tels que normal, Poisson, gamma, inverse gaussienne, les modèles stables-Tweedie multiples sont très fréquents dans les études de statistique et probabilités appliquées. D’abord, nous avons caractérisé les modèles stables-Tweedie normaux à travers leurs fonctions variances ou matrices de covariance exprimées en fonction de leurs vecteurs moyens. La nature des polynômes associés à ces modèles est déduite selon les valeurs de la puissance variance à l’aide des propriétés de quasi orthogonalité, des systèmes de Lévy-Sheffer, et des relations de récurrence polynomiale. Ensuite, ces premiers résultats nous ont permis de caractériser à l’aide de la fonction variance la plus grande classe des stables-Tweedie multiples. Ce qui a conduit à une nouvelle classification laquelle rend la famille beaucoup plus compréhensible. Enfin, une extension de caractérisation des stables-Tweedie normaux par fonction variance généralisée ou déterminant de la fonction variance a été établie via leur propriété d’indéfinie divisibilité et en passant par les équations de Monge-Ampère correspondantes. Exprimées sous la forme de produit des composantes du vecteur moyen aux puissances multiples, la caractérisationde tous les modèles multivariés stables-Tweedie multiples par fonction variance généralisée reste un problème ouvert. / In the framework of natural exponential families, this thesis proposes differents characterizations of multivariate multiple stables-Tweedie under "steepness" property. These models appeared in 2014 in the literature were first introduced and described in a restricted form of the normal stables-Tweedie models before extensions to multiple cases. They are composed by a fixed univariate stable-Tweedie variable having a positive domain, and the remaining random variables given the fixed one are reals independent stables-Tweedie variables, possibly different, with the same dispersion parameter equal to the fixed component. The corresponding normal stables-Tweedie models have a fixed univariate stable-Tweedie and all the others are reals Gaussian variables. Through special cases such that normal, Poisson, gamma, inverse Gaussian, multiple stables-Tweedie models are very common in applied probability and statistical studies. We first characterized the normal stable-Tweedie through their variances function or covariance matrices expressed in terms of their means vector. According to the power variance parameter values, the nature of polynomials associated with these models is deduced with the properties of the quasi orthogonal, Levy-Sheffer systems, and polynomial recurrence relations. Then, these results allowed us to characterize by function variance the largest class of multiple stables-Tweedie. Which led to a new classification, which makes more understandable the family. Finally, a extension characterization of normal stable-Tweedie by generalized variance function or determinant of variance function have been established via their infinite divisibility property and through the corresponding Monge-Ampere equations. Expressed as product of the components of the mean vector with multiple powers parameters reals, the characterization of all multivariate multiple stable- Tweedie models by generalized variance function remains an open problem.