On the statistical estimation of diffusion processes: a survey

Data available on continuos-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).

On the statistical estimation of diffusion processes - a partial survey

Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the employment of Martingale Estimating Functions, and the application of Generalized Method of Moments (GMM).

Pair trading in Bovespa with a quantitative approach: cointegration, Ornstein-Uhlenbeck equation and Kelly criterion.

Pair trading is an old and well-known technique among traders. In this paper, we discuss an important element not commonly debated in Brazil: the cointegration between pairs, which would guarantee the spread stability. We run the Dickey-Fuller test to check cointegration, and then compare the results with non-cointegrated pairs. We found that the Sharpe ratio of cointegrated pairs is greater than the non-cointegrated. We also use the Ornstein-Uhlenbeck equation in order to calculate the half-life of the pairs. Again, this improves their performance. Last, we use the leverage suggested by Kelly Formula, once again improving the results.

A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Avaliação de um método de cromatografia em fase gasosa head space e estudo da estabilidade do etanol em amostras de sangue

The ethanol is the most overused psychoactive drug over the world; this fact makes it one of the main substances required in toxicological exams nowadays. The development of an analytical method, adaptation or implementation of a method known, involves a process of validation that estimates its efficiency in the laboratory routine and credibility of the method. The stability is defined as the ability of the sample of material to keep the initial value of a quantitative measure for a defined period within specific limits when stored under defined conditions. This study aimed to evaluate the method of Gas chromatography and study the stability of ethanol in blood samples, considering the variables time and temperature of storage, and the presence of preservative and, with that check if the conditions of conservation and storage used in this study maintain the quality of the sample and preserve the originally amount of analyte present. Blood samples were collected from 10 volunteers to evaluate the method and to study the stability of ethanol. For the evaluation of the method, part of the samples was added to known concentrations of ethanol. In the study of stability, the other side of the pool of blood was placed in two containers: one containing the preservative sodium fluoride 1% and the anticoagulant heparin and the other only heparin, was added ethanol at a concentration of 0.6 g/L, fractionated in two bottles, one being stored at 4ºC (refrigerator) and another at -20ºC (freezer), the tests were performed on the same day (time zero) and after 1, 3, 7, 14, 30 and 60 days of storage. The assessment found the difference in results during storage in relation to time zero. It used the technique of headspace associated with gas chromatography with the FID and capillary column with stationary phase of polyethylene. The best analysis of chromatographic conditions were: temperature of 50ºC (column), 150ºC (jet) and 250ºC (detector), with retention time for ethanol from 9.107 ± 0.026 and the tercbutanol (internal standard) of 8.170 ± 0.081 minutes, the ethanol being separated properly from acetaldehyde, acetone, methanol and 2-propanol, which are potential interfering in the determination of ethanol. The technique showed linearity in the concentration range of 0.01 and 3.2 g/L (0.8051 x + y = 0.6196; r2 = 0.999). The calibration curve showed the following equation of the line: y = x 0.7542 + 0.6545, with a linear correlation coefficient equal to 0.996. The average recovery was 100.2%, the coefficients of variation of accuracy and inter intra test showed values of up to 7.3%, the limit of detection and quantification was 0.01 g/L and showed coefficient of variation within the allowed. The analytical method evaluated in this study proved to be fast, efficient and practical, given the objective of this work satisfactorily. The study of stability has less than 20% difference in the response obtained under the conditions of storage and stipulated period, compared with the response obtained at time zero and at the significance level of 5%, no statistical difference in the concentration of ethanol was observed between analysis. The results reinforce the reliability of the method of gas chromatography and blood samples in search of ethanol, either in the toxicological, forensic, social or clinic

Long-term stability studies on protection against Newcastle disease by commercial live vaccine used in Brazil

The thermostability (TS) and efficacy offered by live vaccines against Newcastle disease strains B 1, La Sota, VG-GA and Ulster, produced or imported by four Brazilian laboratories, were evaluated during their validity period. Kinetic profiles were obtained from samples conserved in refrigerators during 0, 4, 8, 12, 16, 20 and 24 months after their manufacturing. The statistical analysis of the vaccine titre effect obtained by the fresh air (FA) method showed that the vaccine profiles were parallel and coincident, presenting a significant descending trend. The vaccine titres and efficiency proofs at the end of the validity period were above the level of legislation requirements and showed an average loss in titre of 0.40 and 0.66 log(10), within the first and second validity years, respectively. The titre obtained by TS, within the month after manufacturing, had no significant difference from the titre obtained by FA within 24 months after manufacturing, being their pairs of observations positively correlated (r = 0,49, p = 0.0003), showing that the TS method, which anticipates the vaccines' performance at the end of the validity period, can substitute the FA method 24 months after manufacturing. (C) 2009 The International Association for Biologicals. Published by Elsevier Ltd. All rights reserved.

Stability of multistep second derivative methods for integro-differential equations

The stability of multistep second derivative methods for integro-differential equations is examined through a test equation which allows for the construction of the associated characteristic polynomial and its region of stability (roots in the unit circle) at a proper parameter space. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stability of neutral functional differential equations in terms of measures

In this paper we investigate the relationships between different concepts of stability in measure for the solutions of an autonomous or periodic neutral functional differential equation.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. and third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)