## 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. |

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### 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 |

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analytic characteristic function Appl application asymptotic normality Australian National University branching process C. C. Heyde central limit theorem characteristic function completes the proof condition convergence rates convergence to normality defined denote distributed random variables distribution function domain of attraction E|XT editors estimating functions estimation theory finite variance Galton-Watson process hence identically distributed random independent and identically independent random variables inequality integration invariance principle iterated logarithm L(Bn large numbers law of large Lemma lim inf lim sup log log long-range dependence Maller martingale Math Mathematical maximum likelihood normal distribution obtain optimal paper parameter positive constant Pr(M Pr(S Pr(X Probability and Statistics Probability Theory problem process with immigration proof of Theorem quasi-likelihood random walk rate of convergence satisfied Selected Seneta stable law stationary Stochastic Processes Strassen sums of independent supercritical Suppose verw volume Wiley write