2 edition of Regular variation, extensions and Tauberian theorems found in the catalog.
Regular variation, extensions and Tauberian theorems
J. L. Geluk
Bibliography: p. 129-131.
|Statement||J.L. Geluk, L. de Haan.|
|Series||CWI tract -- 40., CWI tract -- 40.|
|Contributions||Haan, L. de.|
|The Physical Object|
|Pagination||131 p. ;|
|Number of Pages||131|
1. Introduction. Several asymptotic notions play a fundamental role in the theory of generalized functions. The subject has been studied by several authors and applications have been elaborated in areas such as mathematical physics, Tauberian theorems for integral transforms, number theory, and differential by: 5. Second Edition. Springer, p. ISBN: , e-ISBN: Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of.
We introduce a non-regular generalisation of the Nörlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A strong law of large numbers is also proved. Abstract; Open Access Link; Cite. MSC Classification Codes. xx: General. Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles).
Theory of Probability & Its Applications , Weak laws of large numbers in Banach spaces and their extensions. Probability in Banach Spaces, () Stochastic Abelian and Tauberian theorems. Zeitschrift f r Wahrscheinlichkeitstheorie und Verwandte Gebiete , Cited by: A summability method M is regular if it agrees with the actual limit on all convergent series. Such a result is called an Abelian theorem for M, from the prototypical Abel's theorem. More interesting, and in general more subtle, are partial converse results, called Tauberian theorems, from a .
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Regular variation, extensions and Tauberian theorems. [Amsterdam, the Netherlands]: Centrum voor Wiskunde en Informatica, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: J L Geluk; L de Haan. Showing all editions for 'Regular variation, extensions and Tauberian theorems' Sort by: Format; All Formats (13) Book (1) Print book (12) Regular variation, extensions and Tauberian theorems: 1.
Regular variation, extensions and Regular variation theorems. by J L Geluk; L de Haan Print book: English. [Amsterdam, the Netherlands]: Centrum. Regular variation, extensions and Tauberian theorems () Pagina-navigatie: Main; Save publication.
Save as MODS; Export to Mendeley; Save as EndNoteCited by: The book emphasizes such characterizations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather than merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and "second-order" theorems.
Geluk, J.L, & de Haan, L.F.M. Regular variation, extensions and Tauberian by: Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows Regular variation development of the theory from the beginning and his expert commentary evokes.
Tauberian Theory: A Century of Developments Author: Jacob Korevaar Published by Springer Berlin Heidelberg ISBN: DOI: / Table of Contents: The Hardy—Littlewood Theorems Wiener’s Theory Complex Tauberian Theorems Karamata’s Heritage: Regular Variation Extensions of the Classical Theory.
J.L. Geluk, L. de Haan, Regular Variation Extensions and Tauberian Theorems, CWI Tr Amsterdam, Maric V, Radasin Z, Regularly Varying Functions in Asymptotic Analysis; Nikolic A, About two famous results of Jovan Karamata, Archives Internationales d’Histoire des SciencesBorn: February 1,Zagreb, Kingdom of Croatia.
Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results.
He shows the fascination of the difficult Hardy-Littlewood theorems and of an. So far as the later literature on regular variation is concerned, one may perhaps subdivide things by theme. Analysis and Tauberian theory. The book by Korevaar, Tauberian theory—A century of developments, contains a wealth of results, including—Chapter 4, Part 2—a thorough treatment of the role of regular variation within Tauberian by: (), Doeblin (); Gnedenko & Kolmogorov, book, (Russian), (English).
Validity of weak LLN: truncated mean slowly varying. First textbook account with regular variation explicit: Feller, Vol. II, / First textbook account of the mathematical theory: Seneta, Extensions of the Karamata theory and applications to extreme.
"Tauberian theory deals with the problem of finding conditions under which a summable series is actually convergent. A large bibliography and a substantial index round out the book. All in all, this is a well-written, well laid out, interesting monograph, essential to anyone involved in Tauberian theory and related topics.
Highly recommended!"Brand: Springer-Verlag Berlin Heidelberg. One of the difficulties of Tauberian theory is that there are so many different summation methods, and potentially there would be theorems connecting each pair. The organization of the present book is very good and it manages to avoid overwhelming the reader with choices.
Regular variation and probability: The early years Article in Journal of Computational and Applied Mathematics (1) March with 15 Reads How we measure 'reads'Author: Nicholas Bingham. Wiener's Theory.- Complex Tauberian Theorems.- Karamata's Heritage: Regular Variation.- Extensions of the Classical Theory.- Borel Summability and General Circle Methods.- Tauberian Remainder Theory.- References.- Index.
(source: Nielsen Book Data) Tauberian theory compares summability methods for series and integrals, helps to decide when. Q-regular variation and q-difference equations.
Karamata J Sur certain 'Tauberian theorems' de M M Hardy et Littlewood Math. Cluj. 3 33–48 Regular Variation, Extensions and. This chapter discusses the application of regular variation in probability theory.
Regularly varying functions play a role in Tauberian theorems concerning the Laplace transform. A famous theorem of Karamata states that if f is nondecreasing, then f ∈ RV α if fˆ (1/t) ∈ RV α, where fˆ is the Laplace–Stieltjes transform of the function : J.L. Geluk. Y. KASAHARA (): Tauberian theorems of exponential type.
Math. Kyoto Univ. 18, – MathSciNet zbMATH Google Scholar H. KESTEN (): A Cited by: 5. J.L. Geluk, L. de Haan, Regular Variation Extensions and Tauberian Theorems, CWI Tr Amsterdam, Maric V, Radasin Z, Regularly Varying Functions in Asymptotic Analysis Nikolic A, About two famous results of Jovan Karamata, Archives Internationales d’Histoire des SciencesDöd: 14 augusti (65 år).
Jovan Karamata () 3 on uniform approximation of continuous functions by polynomials upon the function f(t) for 0 • t • 1. Here x and f(t) are especially chosen as x = e¡ 1n and f(t) = 0 za 0 • t File Size: KB. L. de Haan ().
On regular variation and its application to the weak convergence of sample extremes. Thesis, University of Amsterdam / Mathematical Centre tract L. de Haan (). A form of regular variation and its application to the domain of attraction of the double exponential distribution.
Z. Wahrscheinlichkeitstheo Finite a and a′ are two series such that there exists a bijection: → such that a i = a′ f(i) for all i, and if there exists some ∈ such that a i = a′ i for all i > N, then A Σ (a) = A Σ (a′).
(In other words, a′ is the same series as a, with only finitely many terms re-indexed.)Note that this is a weaker condition than stability, because any summation method.Renewal processes play an important part in modeling many phenomena in insurance, finance, queuing systems, inventory control and other areas.
In this book, an overview of univariate renewal theory is given and renewal processes in the non-lattice and lattice case are discussed.
A pre-requisite is a basic knowledge of probability theory.