Result: Whittaker-type derivative sampling reconstruction of stochastic Lα(Ω)-processes
Title:
Whittaker-type derivative sampling reconstruction of stochastic Lα(Ω)-processes
Authors:
Source:
Proceedings of the International Symposium on Analytic Function Theory, Fractional Calculus and Their Applications in honour of Professor H.M. Srivastava on his sixty-fifth birth anniversaryApplied mathematics and computation. 187(1):384-394
Publisher Information:
New York, NY: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 21 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Ordre, treillis, structures algébriques ordonnées, Order, lattices, ordered algebraic structures, Analyse mathématique, Mathematical analysis, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Accélération de convergence, Acceleration of convergence, Analyse de l'erreur, Error analysis, Accélération convergence, Convergence acceleration, Aceleración convergencia, Analyse numérique, Numerical analysis, Análisis numérico, Borne supérieure, Upper bound, Cota superior, Calcul erreur, Error analysis, Cálculo error, Convergence, Convergencia, Dérivée fonction, Function derivative, Derivada función, Echantillonnage, Sampling, Muestreo, Erreur troncature, Truncation error, Error truncamiento, Fonction sigma, Sigma function, Función sigma, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Nombre entier, Integer, Entero, Processus stochastique, Stochastic process, Proceso estocástico, Taux convergence, Convergence rate, Relación convergencia, 06Bxx, 65B99, 65Gxx, Analyse erreur, Almost sure P convergence; α-Mean convergence; α-Mean derivatives; Catalan constant; Circular truncation error; Derivative sampling; Karhunen-processes; Lα(Ω, F, P)-Processes; Piranashvili α-processes; Plane sampling reconstruction; Sampling truncation error upper bounds; Weierstraß sigma-function; Whittaker-type sampling formula
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Department of Sciences, Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia
ISSN:
0096-3003
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18796524
Database:
PASCAL Archive
Further Information
Mean square and almost sure Whittaker-type derivative sampling theorems are obtained for the class Lα(Ω, F, P); 0 < α≤ 2 of stochastic processes having spectral representation, with the aid of the Weierstraß σ function. Functions of this class are represented by interpolatory series. The results are valid for harmonizable and stationary processes (a = 2) as well. The formulae are interpreted in the α-mean sense and also in the almost sure P sense when the initial signal function and its derivatives (up to some fixed order) are sampled at the points of the integer lattice Z2. The circular truncation error is introduced and used in the truncation error analysis. Finally, sampling sum convergence rate is provided.