نتایج جستجو برای: hermite polynomials
تعداد نتایج: 41736 فیلتر نتایج به سال:
Dmitrii Karp Institute of Applied Mathematics 7 Radio Street, Vladivostok, 690041, Russia [email protected] Abstra t Let fk be the k-th Fourier oe ient of a fun tion f in terms of the orthonormal Hermite, Laguerre or Ja obi polynomials. We give ne essary and su ient onditions on f for the inequality k |fk|θ < ∞ to hold with θ > 1. As a by-produ t new orthogonality relations for the Hermite and La...
Maximum Likelihood Estimation of Discretely Sampled Diffusions: a Closed-form Approximation Approach
When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very a...
Abstract. We extend Leibniz’ rule for repeated derivatives of a product to multivariate integrals of a product. As an application we obtain expansions for P (a < Y < b) for Y ∼ Np(0, V ) and for repeated integrals of the density of Y . When V −1y > 0 in R the expansion for P (Y < y) reduces to one given by [H. Ruben J. Res. Nat. Bureau Stand. B 68 (1964) 3–11]. in terms of the moments of Np(0, ...
The evaluation of the Hilbert transform of a function is a very important problem that appears widely in science and engineering, specially in signal analysis. In this work, the numerical evaluation of a class of Hilbert transforms using an expansion in terms of Hermite functions, eigenfunctions of the Fourier transform, is performed. Judicious selection of convergence accelerators allows for t...
We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t , this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diag...
Heiligenberg (1987) recently proposed a model to explain how sensory maps could enhance resolution through orderly arrangement of broadly tuned receptors. We have extended this model to the general case of polynomial weighting schemes and proved that the response function is also a polynomial of the same order. We further demonstrated that the Hermitian polynomials are eigenfunctions of the sys...
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