eBook, PDF

Selected Works of C.C. Heyde (eBook, PDF)

Beschreibung

In 1945, very early in the history of the development of a rigorous analytical theory of probability, Feller (1945) wrote a paper called "The fundamental limit theorems in probability" in which he set out what he considered to be "the two most important limit theorems in the modern theory of probability: the central limit theorem and the recently discovered ... 'Kolmogoroff's cel ebrated law of the iterated logarithm' ". A little later in the article he added to these, via a charming description, the "little brother (of the central limit theo rem), the weak law of large numbers", and also the strong law of large num bers, which he considers as a close relative of the law of the iterated logarithm. Feller might well have added to these also the beautiful and highly applicable results of renewal theory, which at the time he himself together with eminent colleagues were vigorously producing. Feller's introductory remarks include the visionary: "The history of probability shows that our problems must be treated in their greatest generality: only in this way can we hope to discover the most natural tools and to open channels for new progress. This remark leads naturally to that characteristic of our theory which makes it attractive beyond its importance for various applications: a combination of an amazing generality with algebraic precision.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 463
• Erscheinungstermin: 17. September 2010
• Englisch
• ISBN-13: 9781441958235
• Artikelnr.: 43732554

Rezensionen

From the reviews:

"This work would be a welcome shelf volume for research workers in probability and statistics and should certainly be a reference available in departmental libraries. ... offers scientists and scholars the opportunity of assembling and commenting upon major classical works in probability and statistics. ... The volume contains 50 original papers, a chronological listing of all publications, as well as individual commentary on particular facets of the research by each of the editors." (Roger Gay, International Statistical Review, Vol. 79 (2), 2011)

"Each editor provided a nice commentary on their respective topics. ... The volume showcased an interesting and informative biography on Heyde and includes a complimentary introduction by the editors and offers a comprehensive bibliography of Heyde's work. ... This is a valuable collection with several useful pieces of statistical and mathematical works and gives the historical developments of such work in their respective fields. Indeed, this collection will be of interest to research scholars in probability, statistics and related fields." (Technometrics, Vol. 53 (2), May, 2011)