Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1576. Advisers: Dejian Lai; Asha S. Kapadia. Includes bibliographical references.

Fines have a very important role in paper chemistry and are a determinant in retention, drainage and the properties of paper. The purpose of this project was to be able to label the fines with fluorophores and study their Brownian motion with fluorescence microscopy. When succeeded this could then be used to study fines, fibers and other additives in a suspension thus giving the fundamental knowledge of why fines have this important role. Due to aggregation of the fines no Brownian motion could be detected. Instead the fines were handled as a network system and small fluorescence labeled latex particles were then studied in this system. This approach yields information about the fines when the obstacle with sedimentation of the network is resolved. / Fines har en viktig roll i papperskemin och har en avgörande roll när det gäller retention, dränering och papprets egenskaper. Syftet med detta projekt var att kunna färga in fines med fluoroforer och sedan följa deras brownska rörelse med hjälp av ett fluorescensmikroskop. Denna metod skulle sedan kunna användas för att observera interaktionerna mellan fines, fibrer och andra additiver i en suspension. Det skulle göra de underliggande mekanismerna kända för varför fines utgör en så viktig del i processen. På grund av att fines aggregerade så fick man istället behandla dem som ett nätverk där man tillsatte redan fluorescerande prober vars rörelser studerades. Att studera fines indirekt på detta vis kommer att ge information när sedimenteringen av nätverket är löst.

GARCH models have been widely used in finance to model volatility ever since the introduction of the ARCH model and its extension to the generalized ARCH (GARCH) model. Lately, there has been growing interest in modelling seasonal volatility, most recently with the introduction of the multiplicative seasonal GARCH models. As an application of the multiplicative seasonal GARCH model with real data, call prices from the major stock market index of India are calculated using estimated parameter values. It is shown that a multiplicative seasonal GARCH option pricing model outperforms the Black-Scholes formula and a GARCH(1,1) option pricing formula. A parametric bootstrap procedure is also employed to obtain an interval approximation of the call price. Narrower confidence intervals are obtained using the multiplicative seasonal GARCH model than the intervals provided by the GARCH(1,1) model for data that exhibits multiplicative seasonal GARCH volatility.

The aim of this PhD Thesis was to build and develop a stochastic calculus (in particular a stochastic integral) with respect to multifractional Brownian motion (mBm). Since the choice of the theory and the tools to use was not fixed a priori, we chose the White Noise theory which generalizes, in the case of fractional Brownian motion (fBm) , the Malliavin calculus. The first chapter of this thesis presents several notions we will use in the sequel.In the second chapter we present a construction as well as the main properties of stochastic integral with respect to harmonizable mBm.We also give Ito formulas and a Tanaka formula with respect to this mBm. In the third chapter we give a new definition, simplier and generalier of multifractional Brownian motion. We then show that mBm appears naturally as a limit of a sequence of fractional Brownian motions of different Hurst index.We then use this idea to build an integral with respect to mBm as a limit of sum of integrals with respect ot fBm. This being done we particularize this definition to the case of Malliavin calculus and White Noise theory. In this last case we compare the integral hence defined to the one we got in chapter 2. The fourth and last chapter propose a multifractional stochastic volatility model where the process of volatility is driven by a mBm. The interest lies in the fact that we can hence take into account, in the same time, the long range dependence of increments of volatility process and the fact that regularity vary along the time.Using the functional quantization theory in order to, among other things, approximate the solution of stochastic differential equations, we can compute the price of forward start options and then get and plot the implied volatility nappe that we graphically represent.

GARCH models have been widely used in finance to model volatility ever since the introduction of the ARCH model and its extension to the generalized ARCH (GARCH) model. Lately, there has been growing interest in modelling seasonal volatility, most recently with the introduction of the multiplicative seasonal GARCH models. As an application of the multiplicative seasonal GARCH model with real data, call prices from the major stock market index of India are calculated using estimated parameter values. It is shown that a multiplicative seasonal GARCH option pricing model outperforms the Black-Scholes formula and a GARCH(1,1) option pricing formula. A parametric bootstrap procedure is also employed to obtain an interval approximation of the call price. Narrower confidence intervals are obtained using the multiplicative seasonal GARCH model than the intervals provided by the GARCH(1,1) model for data that exhibits multiplicative seasonal GARCH volatility.

Rectification phenomena in two specific mesoscopic systems are reviewed. The phenomenon is called ratchet effect, and such systems are called ratchets. In this thesis, particularly a rocked quantum-dot ratchet, and a tunneling ratchet are considered. The origin of the name is explained in a brief historical background. Due to rectification, there is a net non-vanishing electronic current, whose direction can be reversed by changing rocking amplitude, the Fermi energy, or applying magnetic field to the devices (for the rocked ratchet), and tuning the temperature (for the tunneling ratchet). In the last part, a theoretical examination based on the Landauer-B&uuml / ttiker formalism of mesoscopic quantum transport is presented.

This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Kai-Sheng Song, Florida State University,College of Arts and Sciences, Dept. of Statistics; David R. Peterson, Florida State University, College of Business, Dept. of Finance. Title and description from dissertation home page (viewed Sept. 27, 2006). Document formatted into pages; contains ix, 147 pages. Includes bibliographical references.

Este texto apresenta alguns dos elementos básicos envolvidos em um estudo introdutório das equações diferencias estocásticas. Tais equações modelam problemas a tempo contínuo em que as grandezas de interesse estão sujeitas a certos tipos de perturbações aleatórias. Em nosso estudo, a aleatoriedade nessas equações será representada por um termo que envolve o processo estocástico conhecido como Movimento Browniano. Para um tratamento matematicamente rigoroso dessas equações, faremos uso da Integral Estocástica de Itô. A construção dessa integral é um dos principais objetivos do texto. Depois de desenvolver os conceitos necessários, apresentaremos alguns exemplos e provaremos existência e unicidade de solução para equações diferenciais estocásticas satisfazendo certas hipóteses. / This text presents some of the basic elements involved in an introductory study of stochastic differential equations. Such equations describe certain kinds of random perturbations on continuous time models. In our study, the randomness in these equations will be represented by a term involving the stochastic process known as Brownian Motion. For a mathematically rigorous treatment of these equations, we use the Itô Stochastic Integral. The construction of this integral is one of the main goals of the text. After developing the necessary concepts, we present some examples and prove existence and uniqueness of solution of stochastic differential equations satisfying some hypothesis.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-04Bitstream added on 2014-06-13T20:48:05Z : No. of bitstreams: 1 bessada_dfa_me_ift.pdf: 3052096 bytes, checksum: bfe2b25d2283cf5ec06ca7dc7407c70c (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Realizamos neste trabalho uma exposição geral da Teoria do Movimento Browniano, desde suas primeiras observações, feitas no âmbito da Biologia, até sua completa descrição seundo as leis da Mecânica estatística, formulação esta efetuada por Einstein em 1905. Com base nestes princípios físicos analisamos a Teoria do Movimento Browniano de Einstein como sendo um processo estocástico, o que permite sua generalização para um processo de Lévy. Fazemos uma exposição da Teoria de Lévy, e aplicamo-la em seguida na análise de dados provenientes do índice IBOVESPA. Camparamos os resultados com as distribuições empíricas e a modelada via distribuição gaussiana, demonstrando efetivamente que a série financeira analisada apresenta um comportamento não-gaussiano. / Abstracts: We review in this work the foundations of the Theory of Brownian Motion, from the first observations made in Biology to its complete description according to the laws of Statistical Mechanics performed by einstein in 1905. Afterwards we discuss the Einstein's Theory of Brownian Motion as a stochastic process, since this connection allows its generalization to a Lévy process. After a brief review of Lévy Theory we analyse IBOVESPA data within this framework. We compare the outcomes with the empirical and gaussian distributions, showing effectively that the analyzed financial series behaves exactly as a non-gaussian stochastic process.