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Selected Works of C.C. Heyde

  • Book
  • © 2010

Overview

Editors:
  1. Ross Maller

    1. School of Finance & Applied Statistics, Australian National University, Canberra, Australia

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  2. Ishwar Basawa

    1. , Department of Statistics, University of Georgia, Athens, USA

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  3. Peter Hall

    1. Dept. Mathematics & Statistics, University of Melbourne, Melbourne, Australia

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  4. Eugene Seneta

    1. , School of Mathematics and Statistics, University of Sydney, Sydney, Australia

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  • Provides convient access to significant papers from a highly regarded author working at a time when many of the foundational building blocks of probability and statistics were being put in place
  • Includes “author’s pick” of his favorite papers
  • Includes a complete bibliography

Part of the book series: Selected Works in Probability and Statistics (SWPS)

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Table of contents (56 chapters)

  1. Front Matter

    Pages i-xxxvii
    Download chapter PDF

  2. Author’s Pick

    • C. C. Heyde
    Pages 1-1

  3. Chris Heyde’s Contribution to Inference in Stochastic Processes

    • Ishwar Basawa
    Pages 2-4

  4. Chris Heyde’s Work on Rates of Convergence in the Central Limit Theorem

    • Peter Hall
    Pages 5-7

  5. Chris Heyde’s Work in Probability Theory, with an Emphasis on the LIL

    • Ross Maller
    Pages 8-11

  6. Chris Heyde on Branching Processes and Population Genetics

    • Eugene Seneta
    Pages 12-15

  7. On a Property of the Lognormal Distribution

    • C. C. Heyde
    Pages 16-18

  8. Two Probability Theorems and Their Application to Some First Passage Problems

    • C. C. Heyde
    Pages 19-28

  9. Some Renewal Theorems with Application to a First Passage Problem

    • C. C. Heyde
    Pages 29-41

  10. Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables

    • C. C. Heyde
    Pages 42-52

  11. A Contribution to the Theory of Large Deviations for Sums of Independent Random Variables

    • C. C. Heyde
    Pages 53-58

  12. On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law

    • C. C. Heyde
    Pages 59-62

  13. On the Influence of Moments on the Rate of Convergence to the Normal Distribution

    • C. C. Heyde
    Pages 63-70

  14. On Large Deviation Probabilities in the Case of Attraction to a Non-Normal Stable Law

    • C. C. Heyde
    Pages 71-76

  15. On the Converse to the Iterated Logarithm Law

    • C. C. Heyde
    Pages 77-83

  16. A Note Concerning Behaviour of Iterated Logarithm Type

    • C. C. Heyde
    Pages 84-89

  17. On Extended Rate of Convergence Results for the Invariance Principle

    • C. C. Heyde
    Pages 90-91

  18. On the Maximum of Sums of Random Variables and the Supremum Functional for Stable Processes

    • C. C. Heyde
    Pages 92-102

  19. Some Properties of Metrics in a Study on Convergence to Normality

    • C. C. Heyde
    Pages 103-114

  20. Extension of a Result of Seneta for the Super-Critical Galton–Watson Process

    • C. C. Heyde
    Pages 115-118
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Keywords

About this book

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.

Reviews

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)

Editors and Affiliations

  • School of Finance & Applied Statistics, Australian National University, Canberra, Australia

    Ross Maller

  • , Department of Statistics, University of Georgia, Athens, USA

    Ishwar Basawa

  • Dept. Mathematics & Statistics, University of Melbourne, Melbourne, Australia

    Peter Hall

  • , School of Mathematics and Statistics, University of Sydney, Sydney, Australia

    Eugene Seneta

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