Selected Works of C.C. Heyde

ISBN-13: 9781441958228 / Angielski / Twarda / 2010 / 463 str.

Ross Maller; Ishwar Basawa; Peter Hall

Opis

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.

Recenzje

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)

Spis treści

Commentary: Author’s Pick, by C. C. Heyde.- Commentary: Chris Heyde’s Contribution to Inference in Stochastic Processes, by Ishwar Basawa.- Commentary: Chris Heyde’s Work on Rates of Convergence in the Central Limit Theorem, by Peter Hall.- Commentary: Chris Heyde’s Work in Probability Theory, with an Emphasis on the LIL, by Ross Maller.- Commentary: Chris Heyde on Branching Processes and Population Genetics, by Eugene Seneta.- C. C. Heyde. On a property of the lognormal distribution. J. R. Stat. Soc. Ser. B Stat. Methodol. , 25:392–393, 1963. Reprinted with permission of the Royal Statistical Society and John Wiley & Sons.- C. C. Heyde. Two probability theorems and their application to some first passage problems. J. Aust. Math. Soc. , 4:214–222, 1964. Reprinted with permission of the Australian Mathematical Society.- C. C. Heyde. Some renewal theorems with application to a first passage problem. Ann. Math. Statist. , 37:699–710, 1966. Reprinted with permission of the Institute of Mathematical Statistics.- C. C. Heyde. Some results on small-deviation probability convergence rates for sums of independent random variables. Canad. J. Math. , 18:656–665, 1966. Reprinted with the permission of the Canadian Mathematical Society.- C. C. Heyde. A contribution to the theory of large deviations for sums of independent random variables. Z. Wahrsch. Verw. Gebiete. , 7:303–308, 1967. Reprinted with permission of Springer Science+Business Media.- C. C. Heyde. On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Statist. , 38:1575–1578, 1967. Reprinted with permission of the Institute of Mathematical Statistics.- C. C. Heyde. On the influence of moments on the rate of convergence to the normal distribution. Z. Wahrsch. Verw. Gebiete. , 8:12–18, 1967. Reprinted with permission of Springer Science+Business Media.- C. C. Heyde. On large deviation probabilities in the case of attraction to a non-normal stable law. Sankhy Ser. A , 30:253–258, 1968. Reprinted with permission of the Indian Statistical Institute.- C. C. Heyde. On the converse to the iterated logarithm law. J. Appl.Probab. , 5:210–215, 1968. Reprinted with permission of the Applied Probability Trust.- C. C. Heyde. A note concerning behaviour of iterated logarithm type. Proc. Amer. Math. Soc. , 23:85–90, 1969. Reprinted with permission of the American Mathematical Society.- C. C. Heyde. On extended rate of convergence results for the invariance principle. Ann. Math. Statist. , 40:2178–2179, 1969. Reprinted with permission of the Institute of Mathematical Statistics.- C. C. Heyde. On the maximum of sums of random variables and the supremum functional for stable processes. J. Appl. Probab. , 6:419–429, 1969. Reprinted with permission of the Applied Probability Trust.- C. C. Heyde. Some properties of metrics in a study on convergence to normality. Z. Wahrsch. Verw. Gebiete. , 11:181–192, 1969. Reprinted with permission of Springer Science+Business Media.- C. C. Heyde. Extension of a result of Seneta for the super-critical Galton-Watson process. Ann. Math. Statist. , 41:739–742, 1970. Reprinted with permission of the Institute of Mathematical Statistics.- C. C. Heyde. On the implication of a certain rate of convergence to normality. Z. Wahrsch. Verw. Gebiete. , 16:151–156, 1970. Reprinted with permission of Springer Science+Business Media.- C. C. Heyde. A rate of convergence result for the super-critical Galton-Watson process. J. Appl. Probab. , 7:451–454, 1970. Reprinted with permission of the Applied Probability Trust.- C. C. Heyde and B. M. Brown. On the departure from normality of a certain class of martingales. Ann. Math. Statist. , 41:2161–2165, 1970. Reprinted with permission of the Institute of Mathem

Blurb

This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chris’s papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chris’s friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an “author’s pick” of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chris’s publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.