Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On Mean Convergence of Random Fourier - Hermite Series
View through CrossRef
The work in this article is an initiative to explore random Fourier - Hermite series in orthogonal Hermite polynomials. We choose the random coefficients in the series to be the Fourier-Hermite coefficients of a symmetric stable process with weight function , where . The existence of these random coefficients, which we find to be dependent random variables, is established. The random Fourier-Hermite series is proven to be convergent in the sense of mean if the scalars in the series are the Fourier-Hermite coefficients of a function in the weighted space , where the weights are given by with such that . The sum functions of the series is obtained to the stochastic integral .
Title: On Mean Convergence of Random Fourier - Hermite Series
Description:
The work in this article is an initiative to explore random Fourier - Hermite series in orthogonal Hermite polynomials.
We choose the random coefficients in the series to be the Fourier-Hermite coefficients of a symmetric stable process with weight function , where .
The existence of these random coefficients, which we find to be dependent random variables, is established.
The random Fourier-Hermite series is proven to be convergent in the sense of mean if the scalars in the series are the Fourier-Hermite coefficients of a function in the weighted space , where the weights are given by with such that .
The sum functions of the series is obtained to the stochastic integral .
Related Results
Introduction
Introduction
Jean Baptiste Joseph Fourier’s powerful idea of decomposition of a signal into sinusoidal components has found application in almost every engineering and science field. An incompl...
Hermite polynomial normal transformation for structural reliability analysis
Hermite polynomial normal transformation for structural reliability analysis
Purpose
Normal transformation is often required in structural reliability analysis to convert the non-normal random variables into independent standard normal variables. The existi...
Projection estimation for inverses problems on Laguerre and Hermite spaces
Projection estimation for inverses problems on Laguerre and Hermite spaces
Estimation par projection pour des problèmes inverses sur des espaces de Laguerre et d'Hermite
Dans cette thèse, nous développons des procédures d'estimation non pa...
Unbounded Star Convergence in Lattices
Unbounded Star Convergence in Lattices
Let L be a vector lattice, "(" x_α ") " be a L-valued net, and x∈L . If |x_α-x|∧u→┴o 0 for every u ∈〖 L〗_+ then it is said that the net "(" x_α ")" unbounded order converges ...
Stable Hermite transforms via the Golub-Welsch algorithm
Stable Hermite transforms via the Golub-Welsch algorithm
We introduce an efficient and stable algorithm for transforms associated with expansions in Hermite functions interpolated at Hermite polynomial roots. The Hermite transform matrix...
Convergence des ensembles analytiques et des applications méromorphes
Convergence des ensembles analytiques et des applications méromorphes
L'objectif de cette thèse, est l'étude de la convergence d'applications méromorphes entre deux variétés U et X. D'abord nous rappelons trois types de convergence d'applications mér...
Adaptive Slicing Method for Hermite Non-Planar Tessellated Surfaces Models
Adaptive Slicing Method for Hermite Non-Planar Tessellated Surfaces Models
This paper presents an adaptive slicing method for Hermite non-planar tessellated surfaces models to improve the geometric accuracy of Rapid Prototyping (RP). Based on the bending ...
Improvement of conformable fractional Hermite-Hadamard type inequality for convex functions and some new conformable fractional midpoint type inequalities
Improvement of conformable fractional Hermite-Hadamard type inequality for convex functions and some new conformable fractional midpoint type inequalities
In this paper, it is proved that conformable fractional Hermite-Hadamard inequality and conformable fractional Hermite-Hadamard-Fejer inequality is just the results of Hermite-Hada...