| 31/2007 |
On the evaluation of moments for solute transport by random velocity fields Fábio A. Dorini, Fred Furtado, Maria Cristina C. Cunha In this note, we consider the random linear transport equation. We indicate that standard averaging approaches to obtain an equation for the evolution of the statistical mean of the solution may also be valid for all the statistical moments of the solution. With this result we can obtain more statistical information about the random solution, as illustrated in two particular examples.  rp-2007-31.pdf |
| 30/2007 |
Skew Scale Mixture of Normal Distributions: Properties and Estimation Clécio S. Ferreira, Heleno Bolfarine, Víctor H. Lachos Scale mixture of normal distributions are often used as a challenging family for statistical procedures of symmetrical data. In this article, we have defined a skewed version of these distributions and we have derived several of its probabilistic and inferential properties. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine EM algorithms for maximum likelihood estimation. For univariate skewed responses, the EM-type algorithm has been discussed with emphasis on the skew-t, skew-slash, skew-contaminated normal and skew-exponential power distributions. Some simplifying and unifying results are also noted with the Fisher informating matrix, which is derived in closed form for some distributions in the family. Results obtained from simulated and real data sets are reported illustrating the usefulness of the proposed methodology. The main conclusion in reanalyzing a data set previously studied is that the models so far entertained are clearly not the most adequate ones. rp-2007-30.pdf |
| 29/2007 |
On a General Class of Trigonometric Functions and Fourier Series H. Germano Pavão, Edmundo Capelas de Oliveira We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. |
| 28/2007 |
Consistent Estimator for Constrained Minimal Trajectories Ronaldo Dias, Nancy L. Garcia, Adriano Z. Zambom Consider the problem of finding a smooth function joining two points A and B with minimum length constrained to avoid fixed subsets when stochastic measurement errors are present. In this case, the estimator proposed by Dias, Garcia and Zambom (2007) is consistent, in the sense that as the number of observations increases the stochastic trajectory converges to the best deterministic one. Two applications are immediate, searching the optimal a path for an autonomous vehicle while avoiding all fixed obstacles between two points and flight planning to avoid threat or turbulence zones. rp-2007-28.pdf |
| 27/2007 |
Robust Multivariate Measurement Error Model with Skew-Normal/Independent Distributions Víctor H. Lachos, Filidor E. Vilca-Labra, Heleno Bolfarine Skew-normal/independent distributions is a class of asymmetric thicktailed distributions that includes the skew-normal distribution as a especial case. The main virtue of the members of this class of distributions is that they are easy to simulate from and they make it possible to implement the Monte Carlo EM algorithm for maximum likelihood estimation. In this paper, we take skew-normal/independent distributions (Lachos and Vilca, 2007) for the unobserved value of the covariates (latent variable) and symmetric normal/independent (Lange and Sinsheimer, 1993) distributions for the random errors providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Specific distributions examined include univariate and multivariate versions of the skew-normal, the skew-t, the skew-slash and the contaminated skew-normal distribution. The results and methods are applied to a real data set. rp-2007-27.pdf |
| 26/2007 |
HJM Interest Rate Models with Fractional Brownian Motions Alberto M. F. Ohashi, Pedro J. Catuogno In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. We consider the term structure of interest rates as given by a stochastic partial differential equation driven by a cilindrical fractional white noise. We obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs. rp-2007-26.pdf |
| 25/2007 |
Invariant Manifolds for Stochastic PDE with Fractional Brownian Motion Alberto M. F. Ohashi In this work we study invariant manifolds for stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion with parameter $H > 1/2$. The main ingredient in our analysis is the characterization of a controlled deterministic evolution equation where the invariant sets for the SPDE are precisely those of the controlled system. We provide a complete characterization of a given invariant finite dimensional manifold by means of Nagumo-type conditions. rp-2007-25.pdf |
| 24/2007 |
On Sums of Numerical Series and the Fourier Series H. Germano Pavão, Edmundo Capelas de Oliveira We discuss the sums associated with some Fourier series. Some new sums are obtained as particular cases of the Fourier series associated with a convenient class of functions. Two recent results involving numerical series are recovered. |
| 23/2007 |
Grupos de Heisenberg: da Geometria ao Operador de Kohn - Laplace Igor Leite Freire Neste trabalho apresentamos brevemente os Grupos de Heisenberg, algumas de suas propriedades geométricas e a equação semilinear de Kohn - Laplace.Comentamos também resultados recentes envolvendo tais equações e a geometria de $H^{n}$, bem como problemas em aberto envolvendo a estrutura geométrica de $H^{n}$ e grupos de simetrias da equação semilinear de Kohn- Laplace para $n>1$. rp-2007-23.pdf |
| 22/2007 |
Explicit Radial Bratu Solutions in Dimension n = 1, 2 Nir Cohen, Julia V. Toledo-Benavides We find the general solution \(u(x)\), \(x\in \mathbb{R}\) of the 1-D Bratu equation \(u_{xx} + \lambda e^u = 0\) and the general solution \(U(r)\), \(r>0\), of 2-D radial Bratu equation \(rU_{rr} + U_r + \lambda r e^U = 0\) . We use these results to obtain explicit solutions and bifurcation patterns for boundary value problems involving these equations, and in particular, solutions of the Bratu boundary value problem used in combustion theory. We review the history of Liouville's idea which made these results possible, and correct historical errors found in recent literature. rp-2007-22.pdf |
