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Selected Works of C.C. Heyde
On Central Limit and Iterated Logarithm Supplements to the Martingale Convergence Theorem
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Author(s):
C. C. Heyde
Publication date
(Online):
June 24 2010
Publisher:
Springer New York
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Branching Processes
Krishna Athreya
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Peter E. Ney
(1972)
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Dependent Central Limit Theorems and Invariance Principles
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Stochastic Abelian and Tauberian theorems
Ward Whitt
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Book Chapter
Publication date (Print):
2010
Publication date (Online):
June 24 2010
Pages
: 321-338
DOI:
10.1007/978-1-4419-5823-5_42
SO-VID:
16e8f96e-0b95-4bce-9edb-d85106be2e8d
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Book chapters
pp. 1
Author’s Pick
pp. 2
Chris Heyde’s Contribution to Inference in Stochastic Processes
pp. 5
Chris Heyde’s Work on Rates of Convergence in the Central Limit Theorem
pp. 8
Chris Heyde’s Work in Probability Theory, with an Emphasis on the LIL
pp. 12
Chris Heyde on Branching Processes and Population Genetics
pp. 16
On a Property of the Lognormal Distribution
pp. 19
Two Probability Theorems and Their Application to Some First Passage Problems
pp. 29
Some Renewal Theorems with Application to a First Passage Problem
pp. 42
Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables
pp. 53
A Contribution to the Theory of Large Deviations for Sums of Independent Random Variables
pp. 59
On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law
pp. 63
On the Influence of Moments on the Rate of Convergence to the Normal Distribution
pp. 71
On Large Deviation Probabilities in the Case of Attraction to a Non-Normal Stable Law
pp. 77
On the Converse to the Iterated Logarithm Law
pp. 84
A Note Concerning Behaviour of Iterated Logarithm Type
pp. 90
On Extended Rate of Convergence Results for the Invariance Principle
pp. 92
On the Maximum of Sums of Random Variables and the Supremum Functional for Stable Processes
pp. 103
Some Properties of Metrics in a Study on Convergence to Normality
pp. 115
Extension of a Result of Seneta for the Super-Critical Galton–Watson Process
pp. 119
On the Implication of a Certain Rate of Convergence to Normality
pp. 125
A Rate of Convergence Result for the Super-Critical Galton-Watson Process
pp. 129
On the Departure from Normality of a Certain Class of Martingales
pp. 134
Some Almost Sure Convergence Theorems for Branching Processes
pp. 138
Some Central Limit Analogues for Supercritical Galton-Watson Processes
pp. 147
An Invariance Principle and Some Convergence Rate Results for Branching Processes
pp. 159
Improved classical limit analogues for Galton-Watson processes with or without immigration
pp. 170
Analogues of Classical Limit Theorems for the Supercritical Galton-Watson Process with Immigration
pp. 181
On Limit Theorems for Quadratic Functions of Discrete Time Series
pp. 191
Martingales: A Case for a Place in the Statistician’s Repertoire
pp. 200
On the Influence of Moments on Approximations by Portion of a Chebyshev Series in Central Limit Convergence
pp. 214
Estimation Theory for Growth and Immigration Rates in a Multiplicative Process
pp. 237
An Iterated Logarithm Result for Martingales and its Application in Estimation Theory for Autoregressive Processes
pp. 249
On the Uniform Metric in the Context of Convergence to Normality
pp. 262
Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary Increments
pp. 271
An Iterated Logarithm Result for Autocorrelations of a Stationary Linear Process
pp. 276
On Estimating the Variance of the Offspring Distribution in a Simple Branching Process
pp. 289
A Nonuniform Bound on Convergence to Normality
pp. 294
Remarks on efficiency in estimation for branching processes
pp. 301
The Genetic Balance between Random Sampling and Random Population Size
pp. 305
On a unified approach to the law of the iterated logarithm for martingales
pp. 318
The Effect of Selection on Genetic Balance when the Population Size is Varying
pp. 321
On Central Limit and Iterated Logarithm Supplements to the Martingale Convergence Theorem
pp. 339
A Log Log Improvement to the Riemann Hypothesis for the Hawkins Random Sieve
pp. 345
On an Optimal Asymptotic Property of the Maximum Likelihood Estimator of a Parameter from a Stochastic Process
pp. 355
On Asymptotic Posterior Normality for Stochastic Processes
pp. 361
On the Survival of a Gene Represented in a Founder Population
pp. 370
An alternative approach to asymptotic results on genetic composition when the population size is varying
pp. 376
On the Asymptotic Equivalence of L p Metrics for Convergence to Normality
pp. 386
Quasi-likelihood and Optimal Estimation
pp. 400
Fisher Lecture
pp. 411
On Best Asymptotic Confidence Intervals for Parameters of Stochastic Processes
pp. 416
A quasi-likelihood approach to estimating parameters in diffusion-type processes
pp. 424
Asymptotic Optimality
pp. 426
On Defining Long-Range Dependence
pp. 438
Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency
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