Made available in DSpace on 2014-12-17T15:14:51Z (GMT). No. of bitstreams: 1 JoaoMS.pdf: 634960 bytes, checksum: 579213d21eb24a6a8d342d2c3b15bc3d (MD5) Previous issue date: 2003-06-20 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work we investigate the stochastic behavior of a large class of systems with variable damping which are described by a time-dependent Lagrangian. Our stochastic approach is based on the Langevin treatment describing the motion of a classical Brownian particle of mass m. Two situations of physical interest are considered. In the first one, we discuss in detail an application of the standard Langevin treatment (white noise) for the variable damping system. In the second one, a more general viewpoint is adopted by assuming a given expression to the so-called collored noise. For both cases, the basic diffententiaql equations are analytically solved and al the quantities physically relevant are explicitly determined. The results depend on an arbitrary q parameter measuring how the behavior of the system departs from the standard brownian particle with constant viscosity. Several types of sthocastic behavior (superdiffusive and subdiffusive) are obteinded when the free pamameter varies continuosly. However, all the results of the conventional Langevin approach with constant damping are recovered in the limit q = 1 / Neste trabalho n?s investigamos o comportamento estoc?stico de uma grande classe de sistemas com amortecimento vari?vel descritos por uma lagraniana dependente do tempo. Nossa abordagem estoc?stica ? baseada no formalismo de Langevin descrevendo o comportamento de uma part?cula browniana cl?ssica de massa m. Duas situa??es de interesse f?sico s?o consideradas. Inicialmente, uma aplica??o do tratamento padr?o de Langevin (ru?do branco) para viscosidade vari?vel ? discutido em detalhe. Na segunda abordagem, um ponto de vista mais geral ? adotado supondo uma dada express?o para o chamado ru?do branco. Em ambos os casos as equa??es diferenciais b?sicas s?o analiticamente resolvidas, e todas as quantidades fisicamente relevantes s?o explicitamente determinadas. Os resultados dependem de um par?metro arbitr?rio (q) medindo como o comportamento din?mico do sistema se afasta daquele apresentado pela part?cula browniana com viscosidade constante. V?rios tipos de comportamentos estoc?sticos (subsifusivos and superdifusivos) s?o obtidos quando o par?metro livre q varia continuamente. Contudo, no limite q -> 1, todos os resultados da abordagem de Langevin convencional s?o recuperados

Magister Scientiae - MSc / This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric Brownian motion time series should be characterised by the Hurst exponent of ½. A value of a Hurst exponent different from that would indicate the presence of long memory or fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added. / South Africa

The financial market is a stochastic and complex system that is challenging to model. It is crucial for investors to be able to model the probability of possible outcomes of financial investments and financing decisions in order to produce fruitful and productive investments. This study investigates how Monte Carlo simulations of random walks can be used to model the probability of future stock returns and how the simulations can be improved in order to provide better accuracy. The implemented method uses a mathematical model called Geometric Brownian Motion (GBM) in order to simulate stock prices. Ten Swedish large-cap stocks were used as a data set for the simulations, which in turn were conducted in time periods of 1 month, 3 months, 6 months, 9 months and 12 months. The two main parameters which determine the outcome of the simulations are the mean return of a stock and the standard deviation of historical returns. When these parameters were calculated without weights the method proved to be of no statistical significance. The method improved and thereby proved to be statistically significant for predictions for a 1 month time period when the parameters instead were weighted. By varying the assumptions regarding price distribution with respect to the size of the current time period and using other weights, the method could possibly prove to be more accurate than what this study suggests. Monte Carlo simulations seem to have the potential to become a powerful tool that can expand our abilities to predict and model stock prices. / Den finansiella marknaden är ett stokastiskt och komplext system som är svårt att modellera. Det är angeläget för investerare att kunna modellera sannolikheten för möjliga utfall av finansiella investeringar och beslut för att kunna producera fruktfulla och produktiva investeringar. Den här studien undersöker hur Monte Carlo-simuleringar av så kallade random walks kan användas för att modellera sannolikheten för framtida aktieavkastningar, och hur simuleringarna kan förbättras för att ge bättre precision. Den implementerade metoden använder den matematiska modellen Geometric Brownian Motion (GBM) för att simulera aktiepriser. Tio svenska large-cap aktier valdes ut som data för simuleringarna, som sedan gjordes för tidsperioderna 1 månad, 3 månader, 6 månader, 9 månader och 12 månader. Huvudparametrarna som bestämmer utfallet av simuleringarna är medelvärdet av avkastningarna för en aktie samt standardavvikelsen av de historiska avkastningarna. När dessa parametrar beräknades utan viktning gav metoden ingen statistisk signifikans. Metoden förbättrades och gav då statistisk signifikans på en 1 månadsperiod när parametrarna istället var viktade. Metoden skulle kunna visa sig ha högre precision än vad den här studien föreslår. Det är möjligt att till exempel variera antagandena angående prisernas fördelning med avseende på storleken av den nuvarande tidsperioden, och genom att använda andra vikter. Monte Carlo-simuleringar har därför potentialen att utvecklas till ett kraftfullt verktyg som kan öka vår förmåga att modellera och förutse aktiekurser.

Ce mémoire étudie le comportement des particules dont la position est maximale au temps t dans la marche aléatoire branchante et le mouvement brownien branchant sur R, pour des valeurs de t grandes. Plus exactement, on regarde le comportement du maximum d’une marche aléatoire branchante dans un environnement inhomogène en temps, au sens où la loi des accroissements varie en fonction du temps. On compare avec des modèles connus ou simplifiés, en particulier le modèle i.i.d., où l’on observe des marches aléatoires indépendantes et le modèle de la marche aléatoire homogène. On s’intéresse par la suite aux corrélations entre les particules maximales d’un mouvement brownien branchant. Plus précisément, on étudie le temps de branchement entre deux particules maximales. Finalement, on applique les méthodes et les résultats des premiers chapitres afin d’étudier les corrélations dans un mouvement brownien branchant dans un environnement inhomogène. Le résultat principal du mémoire stipule qu’il y a existence de temps de branchement au centre de l’intervalle [0, t] dans le mouvement brownien branchant inhomogène, ce qui n’est pas le cas pour le mouvement brownien branchant standard. On présentera également certaines simulations numériques afin de corroborer les résultats numériques et pour établir des hypothèses pour une recherche future. / This thesis studies the behavior of particles that are maximal at time t in branching random walk and branching Brownian motion on R, for large values of t. Precisely, we look at the behavior of the maximum in a branching random walk in a time-inhomogeneous environment, where the law of the increments varies with respect to time. We compare with known or simplified models such as the model where random walks are taken to be i.i.d. and the branching random walk in a time-homogeneous environment model. We then take a look at the correlations between maximal particles in a branching brownian motion. Specifically, we look at the branching time between those maximal particles. Finally, we apply results and methods from the first chapters to study those same correlations in branching Brownian motion in a inhomogeneous environment. The thesis’ main result establishes existence of branching time at the center of the interval [0, t] for the branching Brownian motion in a inhomogeneous environment, which is not the case for standard branching brownian motion.We also present results of simulations that agree with theoretical results and help establishing new hypotheses for future research.

La surexposition aux rayonnements ionisants est actuellement une préoccupation croissante des cliniciens. Lors d'une exposition externe, la peau est le premier tissu lésé. Or, il n'existe pas d'outil fiable qui permette de diagnostiquer l'atteinte tissulaire. L'objectif de ce travail est donc de montrer la possibilité d'utiliser une méthode non invasive pour l'aide in vivo au diagnostic et au pronostic du syndrome cutané d'irradiation aigüe. La première partie de ce travail concerne le choix de la méthode d'investigation. L'interaction entre une lumière cohérente et un milieu diffusant engendre un phénomène d'interférence appelé speckle. Une analyse fréquentielle classique sur le champ de speckle est complétée par une approche stochastique pour en extraire des paramètres caractérisant les figures de speckle. Dans la deuxième partie le protocole expérimental a été testé afin de mieux comprendre le comportement des paramètres en fonciton de quelques propriétés physiques de milieux diffusants synthétiques. Cette étude a révélé que certains des paramètres du speckle étaient plus influencés par les gros diffuseurs (Mie) alors que d'autres l'étaient par les plus petits (Rayleigh). La troisième partie concerne l'application de cette méthode in vivo au syndrome cutané d'irradiation aigüe chez le porc. L'analyse des résultats acquis lors du suivi de plusieurs animaux montre la possibilité de discriminer les zones irradiées des zones saines plusieurs semaines avant l'apparition des premiers signes cliniques. Enfin, pour comprendre les résultats obtenus sur la brûlure radiologique, nous avons confronté l'ensemble des résultats physiques et ceux obtenus par les analyses histologiques. / Overexposure to ionizing radiation is now a growing concern of clinicians. In case of external exposure, the skin is the first tissue exposed. However, there are no tools that can diagnose pathological tissue. The objective of this work is to demonstrate the possibility of using a non-invasive method for in vivo diagnosis and prognosis of acute cutaneous radiation syndrome. The first part of this work concerns the choice of the investigation method. Interaction of coherent light and scattering medium creates a phenomenon called speckle. A classical frequential analysis on the spekle field is supplemented by a stochastic approach to extract parameters characterizing speckle patterns. In the second part, the experimental setup has been tested in order to understand the parameters behavior in function of some physical properties of synthetic scattering media. The study revealed that some of the speckle parameters were more influenced by big scatterers (Mie) while others were by the smallest (Rayleigh). The third part concerns the in vivo application of this method on acute cutaneous radiation syndrome in pigs. Analysis of the results gained during the monitoring of several animals showeb the ability to discriminate between irradiated and healthy zones several weeks before apparition of firsts clinical signs. Finally, in order to understand the results on the radiological burn, we have confronted all physical results and those obtained by histological analyses.

Après le génome, le nouveau défi est celui du protéome. Nous avons progressé vers la mise au point de la séparation électrophorétique des protéines membranaires dans un milieu qui leur conviendrait, type bicouche lipidique supportée. La grandeur principale, mesurée par FRAPP, a été le coefficient de diffusion de lipides ainsi que des protéines. L'étude du comportement de la bicouche supportée a permis de mettre en évidence, pour certains supports et dans certaines conditions de température, la formation d'une phase ondulée (ou ripple) malgré la proximité du support. La diminution de la portée des interactions coulombiennes par adjonction de sel se traduit par une augmentation de plusieurs ordres de grandeur du coefficient de diffusion, approchant au final le comportement d'une bicouche libre, tout en conservant les étapes caractéristiques de la transition gel/fluide. L'ordre de grandeur de ces énergies d'interactions a été estimé à partir des courbes D= f(T) et validé par une étude préliminaire originale de DSC sur des bicouches lipidiques supportées. L'α-Hémolysine s'insère spontanément sous forme d'un pore heptamérique dans nos bicouches supportées et diffuse librement. En l'incubant en phase mixte (zones gel+ zones fluide), nous observons la formation de complexes de protéines. La dépendance du coefficient de diffusion avec la taille de l'objet est en 1/R2, R étant le rayon équivalent de la partie insérée de l'objet. L'application d'un champ électrique montre un transport électrophorétique dont la direction et l'importance sont modulées par la charge de l'objet. La mobilité électrophorétique varie également en 1/R2. / After the genome, the new challenge is the proteome. We have progressed toward electrophoretic separation of membrane proteins in a medium that they love, a supported lipid bilayer. The main parameter, measured by FRAPP, was the diffusion coefficient of different objects (lipids, proteins). Studying bilayer behaviour has showed that, on particular supports and in a given temperature range, ripple phase can exist, despite the proximity of the support. Adding salt decreases coulombic interactions which turns to increase the diffusion coefficient over several orders of magnitude, reaching the value for a free-standing bilayer in the fluid phase, meanwhile the main characteristic steps of the global gel/fluid transition are still observed. Estimation of the value of the interaction energy has been made and compared to results of a preliminary DSC study. α-Hémolysin self-inserts spontaneously as an heptameric pore in supported bilayers and diffuses freely. Incubating in a gel/fluid mixture leads to protein complex formation. Diffusion varies with size as 1/R2, R being the equivalent radius of the inserted part of the object. Applying an electric field results in an electrophoretic motion where direction and magnitude are modulated by the charge of the object. Electrophoretic mobility varies also as 1/R2. Size dependence, magnitude of mobilities and a simple building protocol allow to hope carrying out soon a real electrophoretic separation of a protein mixture.

La statistique des valeurs extrêmes est une question majeure dans divers contextes scientifiques. Cependant, bien que la description de la statistique d'un extremum global soit certainement une caractéristique importante, celle-ci ne se concentre que sur une seule variable parmi un grand nombre de variables aléatoires. Une question naturelle qui se pose alors est la suivante: ces valeurs extrêmes sont-elles isolées, loin des autres variables ou bien au contraire existe-t-il un grand nombre d'autres variables proches de ces valeurs extrêmes ? Ces questions ont suscité l'étude de la densité d'état de ces événements quasi-extrêmes. Il existe pour cette quantité peu de résultats pour des variables fortement corrélées, qui est pourtant le cas rencontré dans de nombreux modèles fondamentaux. Deux pistes de modèles physiques de variables fortement corrélées pouvant être étudiés analytiquement se démarquent alors: les positions d’une marche aléatoire et les valeurs propres de matrice aléatoire. Cette thèse est ainsi consacrée à l’étude de statistique d’extrêmes pour ces deux modèles de variables fortement corrélées. Dans une première partie, j’étudie le cas où la collection de variables aléatoires est la position au cours du temps d’un mouvement brownien, qui peut être contraint à être périodique, positif... Ce mouvement brownien est vu comme la limite d’un marcheur aléatoire classique après un grand nombre de pas. Il est alors possible d’interprèter ce problème comme celui d’une particule quantique dans un potentiel ce qui permet d’utiliser des méthodes puissantes issues de la mécanique quantique comme l’utilisation de propagateurs et de l’intégrale de chemin. Ces outils permettent de calculer la densité moyenne à partir du maximum pour les différents mouvements browniens contraints et même la distribution complète de cette quantité pour certains cas. Il est également possible de généraliser cette démarche à l’étude de plusieurs marches aléatoires indépendantes ou avec interaction. Cette démarche permet également d’effectuer une étude temporelle, ainsi que de généraliser à l’étude d’autres fonctionnelle du maximum. Dans la seconde partie, j’étudie le cas où la collection de variables aléatoires est composée des valeurs propres d’une matrice aléatoire. Ce travail se concentre sur l’études des matrices des ensembles gaussiens (GOE, GUE et GSE) ainsi qu’à l’étude des matrices de Wishart. L’étude du voisinage de la valeur propre maximale pour ces deux modèles est faite en utilisant une méthode fondée sur les propriétés des polynômes orthogonaux. Dans le cas des matrices gaussiennes unitaires GUE, j’ai obtenu une formule analytique pour la distribution à partir du maximum ainsi qu’une nouvelle expression de la statistique du gap entre les deux plus grandes valeurs propres en termes d’une fonction transcendante de Painlevé. Ces résultats, et plus particulièrement leurs généralisations aux cas GOE, sont alors appliqués à un modèle de verre de spin sphérique en champs moyen. Dans le cas des matrices de Wishart, l’analyse des polynômes orthogonaux dans le régime de double échelle m’a permis de retrouver les différentes statistiques de la valeur propre minimale et également de prouver une conjecture sur la première correction de taille finie pour des grandes matrices de la distribution de la valeur propre minimale dans la limite dite de «hard edge». / Extreme value statistics plays a keyrole in various scientific contexts. Although the description of the statistics of a global extremum is certainly an important feature, it focuses on the fluctuations of a single variable among many others. A natural question that arises is then the following: is this extreme value lonely at the top or, on the contrary, are there many other variables close to it ? A natural and useful quantity to characterize the crowding is the density of states near extremes. For this quantity, there exist very few exact results for strongly correlated variables, which is however the case encountered in many situations. Two physical models of strongly correlated variables have attracted much attention because they can be studied analytically : the positions of a random walker and the eigenvalues of a random matrix. This thesis is devoted to the study of the statistics near the maximum of these two ensembles of strongly correlated variables. In the first part, I study the case where the collection of random variables is the position of a Brownian motion, which may be constrained to be periodic or positive. This Brownian motion is seen as the limit of a classical random walker after a large number of steps. It is then possible to interpret this problem as a quantum particle in a potential which allows us to use powerful methods from quantum mechanics as propagators and path integral. These tools are used to calculate the average density from the maximum for different constrained Brownian motions and the complete distribution of this observable in certain cases. It is also possible to generalize this approach to the study of several random walks, independent or with interaction, as well as to the study of other functional of the maximum. In the second part, I study the case of the eigenvalues of random matrices, belonging to both Gaussian and Wishart ensembles. The study near the maximal eigenvalues for both models is performed using a method based on semi-classical orthogonal polynomials. In the case of Gaussian unitary matrices, I have obtained an analytical formula for the density near the maximum as well as a new expression for the distribution of the gap between the two largest eigenvalues. These results, and in particular their generalizations to different Gaussian ensembles, are then applied to the relaxational dynamics of a mean-field spin glass model. Finally, for the case of Wishart matrices I proposed a new derivation of the distribution of the smallest eigenvalue using orthogonal polynomials. In addition, I proved a conjecture on the first finite size correction of this distribution in the «hard edge» limit.

[pt] Deposição de parafinas é um dos mais críticos problemas operacionais no transporte de óleo cru, nos dutos que operam em ambientes frios. Portanto, uma predição acurada da deposição de parafinas é crucial para o projeto eficiente de linhas submarinas. Infelizmente, a deposição de parafinas é um processo complexo e os mecanismos de deposição ainda não são bem compreendidos. Visando identificar a importância relativa dos diferentes mecanismos de deposição, dois deles foram investigados: Difusão Molecular e Browniana. Para determinar a quantidade de depósito, as equações de conservação de massa, quantidade de movimento linear, energia, concentração da mistura e concentração da parafina fora da solução foram resolvidas numericamente pelo método de volumes finitos. Um sistema de coordenadas móveis não ortogonais que se adapta a interface do depósito da parafina foi empregado. Apesar da obtenção de uma concordância razoável do perfil de depósito, obtido com os mecanismos selecionados no regime laminar, com resultados disponíveis na literatura, uma discrepância significativa foi observada durante o transiente. O emprego do mecanismo de difusão browniana levou a uma pequena melhora na predição da solução nas regiões sub- resfriadas. A influência do regime turbulento como o mecanismo de difusão molecular também foi investigado, empregando o modelo de turbulência para baixo Reynolds K- (Taxa de dissipação viscosa da energia cinética turbulenta).Os resultados obtidos apresentaram coerência física, com uma taxa menor de aumento do depósito com o tempo, pois a região próxima à interface com temperatura abaixo da temperatura de aparecimento de cristais é menor no regime turbulento. / [en] Wax deposition is one of the major critical operational problems in crude oil pipelines operating in cold environments. Therefore, accurate prediction of the wax deposition is crucial for the efficient design of subsea lines. Unfortunately, wax deposition is a complex process for which the mechanisms are still not fully understood. Aiming at the identification of the relative importance of the different deposition mechanisms, two of them were investigated: Molecular and Brownian Diffusion. To determine the amount of deposit, the conservation equations of mass, momentum, energy, concentration of the mixture and wax concentration outside the solution were numerically solved with the finite volume method. A non-orthogonal moving coordinate system that adapts to the wax interface deposit geometry was employed. Although for the laminar regime, the deposition profile predicted with the selected deposition mechanisms presented a reasonable agreement with available literature results for the steady state regime, a significant discrepancy was observed during the transient. The employment of the Brownian diffusion mechanism led to only a small improvement in the transient solution prediction in sub-cooled regions. The influence of the turbulent regime with the Molecular diffusion mechanism was also investigated by employing the Low Reynolds ê−turbulence model. The results obtained were physically coherent, presenting a smaller deposit thickness, since the region with temperature below the wax appearance temperature is smaller in the turbulent regime.

Nesta dissertação desenvolvemos o Cálculo Estocástico para provar teoremas clássicos de Análise Complexa, em particular, o pequeno teorema de Picard. / In this dissertation we develop the Stochastic Calculus for to prove classical theorems in Complex Analysis, in particular, the little Picard\'s theorem.

Nesta dissertação desenvolvemos o Cálculo Estocástico para provar teoremas clássicos de Análise Complexa, em particular, o pequeno teorema de Picard. / In this dissertation we develop the Stochastic Calculus for to prove classical theorems in Complex Analysis, in particular, the little Picard\'s theorem.