Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memory

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Complex-valued b-spline neural networks for modelling and inverse of wiener systems

Communication signal processing applications often involve complex-valued (CV) functional representations for signals and systems. CV artificial neural networks have been studied theoretically and applied widely in nonlinear signal and data processing [1–11]. Note that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchy-Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons (MLP) [4]. A fully CV radial basis function (RBF) nework was introduced in [8] for regression and classification applications. Alternatively, the problem can be avoided by using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A even more challenging problem is the inverse of a CV

Processus stochastiques en finance (2ème partie)

Este documento é um texto didático destinado aos estudantes e pesquisadores em econometria e finanças. Baseia-se na experiência dos autores em cursos de pós-graduação na ULB, Bruxelles e na FGV IEPGE, Rio. Não há a pretensão de rigor matemático, e nem a de cobrir todas as aplicações financeiras da teoria dos processos estocásticos. Esta segunda parte discute as medidas equivalentes de martingale e o resultado de Girsanov, a sua aplicação ao modelo de Black-Scholes e a questão da avaliação de um call europeu.

Processus stochastiques en finance (1ère partie)

Este documento é um texto didático destinado aos estudantes e pesquisadores em econometria e finanças. Baseia-se na experiência dos autores em cursos de pós-graduação nos dois lados do Atlântico: na ULB, Bruxelles e na FGV IEPGE, Rio. Não há a pretensão de rigor matemático, e nem a de cobrir todas as aplicações financeiras da teoria dos processos estocásticos. Esta primeira parte discute as martingales e o movimento browniano, os processos de difusão e a integral estocástica, o lema de Itô e o modelo de Black e Scholes.

Transformation du processus de production dans un climat d'équité

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Equité et transformation du processus de production: une approche intégrée

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Le régionalisme ouvert en Amérique latine et aux Caraïbes: l'intégration économique au service de la transformation du processus de production dans un climat d'équité

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