Vacca-type series for values of the generalized Euler constant function and its derivative.
Vaidya's preconditioners: Implementation and experimental study.
Valeurs des ondelettes aux bords d'un intervalle
Validation of numerical simulations of a simple immersed boundary solver for fluid flow in branching channels
This work deals with the flow of incompressible viscous fluids in a two-dimensional branching channel. Using the immersed boundary method, a new finite difference solver was developed to interpret the channel geometry. The numerical results obtained by this new solver are compared with the numerical simulations of the older finite volume method code and with the results obtained with OpenFOAM. The aim of this work is to verify whether the immersed boundary method is suitable for fluid flow in channels...
Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models
In testing that a given distribution Pbelongs to a parameterized family , one is often led to compare a nonparametric estimateAn of some functional A of P with an element Aθn corresponding to an estimate θn of θ. In many cases, the asymptotic distribution of goodness-of-fit statistics derived from the process n1/2(An−Aθn) depends on the unknown distribution P. It is shown here that if the sequences An and θn of estimators are regular in some sense, a parametric bootstrap approach yields valid approximations...
Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets
This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic spline-wavelet...
Valuing barrier options using the adaptive discontinuous Galerkin method
This paper is devoted to barrier options and the main objective is to develop a sufficiently robust, accurate and efficient method for computation of their values driven according to the well-known Black-Scholes equation. The main idea is based on the discontinuous Galerkin method together with a spatial adaptive approach. This combination seems to be a promising technique for the solving of such problems with discontinuous solutions as well as for consequent optimization of the number of degrees...
Variable metric method with limited storage for large-scale unconstrained minimization
Variable metric methods for a class of extended conic functions
Variable multistep methods
Variable-precision arithmetic considered perilous - a detective story.
Variance function estimation via model selection
The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted...
Variance reduction in a stochastic volatility scenario.
Variances in spectral analysis of membrane noise
Le fluttuazioni di conduttanza di un modello di canale del potassio di una fibra muscolare che segue una cinetica di Hodgkin e Huxley sono state analizzate attraverso l'analisi spettrale indiretta. Sono state confrontate due diverse stime della densità spettrale e le loro rispettive varianze: quella della prima stima considerata è già nota, mentre quella della seconda stima è stata ricavata da noi nelle medesime ipotesi (distribuzione normale). I risultati teorici sono stati confrontati con quelli...
Variantes sur un théorème de Candès, Romberg et Tao
Le théorème CRT dit comment reconstruire un signal à partir d’un échantillonnage de fréquences parcimonieux. L’hypothèse sur le signal, considéré comme porté par un groupe cyclique d’ordre , est qu’il est porté par un petit nombre de points, , et la méthode est de choisir aléatoirement fréquences et de minimiser dans l’algèbre de Wiener le prolongement à de la transformée de Fourier du signal réduite à ces fréquences. Quand est grand, la probabilité de reconstruire le signal est voisine...
Variational analysis for the Black and Scholes equation with stochastic volatility
We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...
Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
We propose a variational analysis for a Black and Scholes equation with stochastic volatility. This equation gives the price of a European option as a function of the time, of the price of the underlying asset and of the volatility when the volatility is a function of a mean reverting Orstein-Uhlenbeck process, possibly correlated with the underlying asset. The variational analysis involves weighted Sobolev spaces. It enables to prove qualitative properties of the solution, namely a maximum principle...
Variational and boundary value problems for differential equations with deviating argument
Variational approximation methods for eigenvalues. Convergence theorems
Variational approximation of flux in conforming finite element methods for elliptic partial differential equations : a model problem
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.