International Conference Of The Forum For Interdisciplinary Mathematics On Combinatorics Information Theory And Statistics

Author : Ross Maller
Publisher : Springer Science & Business Media
ISBN 13 : 1441958231
Total Pages : 490 pages
Book Rating : 4.4/5 (419 download)

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Download or read book Selected Works of C.C. Heyde written by Ross Maller and published by Springer Science & Business Media. This book was released on 2010-09-17 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.