Selected Works of C.C. HeydeRoss Maller, Ishwar Basawa, Peter Hall, Eugene Seneta 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. |
Contents
Emphasis on the LIL by Ross Maller | 8 |
B Stat Methodol 25392393 1963 Reprinted with permission | 16 |
problem Ann Math Statist 37699710 1966 Reprinted with permis | 29 |
656 | 42 |
with permission of Springer Science+Business Media | 63 |
210215 1968 Reprinted with permission of the Applied | 77 |
5259 1971 Reprinted with per | 138 |
Mathematical Society | 155 |
19 1972 invited paper Reproduced with | 190 |
tion in estimation theory for autoregressive processes J Appl Probab | 236 |
Wiley Sons | 354 |
97 | 376 |
J Gao V Anh and C Heyde Statistical estimation of nonstationary | 438 |
Other editions - View all
Selected Works of C.C. Heyde Ross Maller,Ishwar Basawa,Peter Hall,Eugene Seneta No preview available - 2016 |
Selected Works of C.C. Heyde Ross Maller,Ishwar Basawa,Peter Hall,Eugene Seneta No preview available - 2010 |
Selected Works of C.C. Heyde Ross Maller,Ishwar Basawa,Peter Hall,Eugene Seneta No preview available - 2010 |
Common terms and phrases
Appl application assumption asymptotic attraction Australian bound branching process C. C. Heyde central limit theorem characteristic function Chris condition consider continuous convergence corresponding defined denote dependence difference discussion distribution editors equivalent establish estimating functions estimation theory example exists extended fact finite follows given gives hence holds identically distributed immigration independent and identically inequality Inference integration iterated logarithm Lemma likelihood log log martingale Math Mathematical mean methods moments numbers obtain optimal parameter population possible Pr(S Pr(X probability problem proof proof of Theorem properties random variables rate of convergence References respect result satisfied Selected Seneta sequence stable stationary Statist Stochastic Processes sufficient sums Suppose surely theory University variance volume write York zero