Mixing Sequences Of Random Variables And Probabilistic Number Theory
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Mixing Sequences Of Random Variables And Probabilistic Number Theory
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Author : Walter Philipp
language : en
Publisher: American Mathematical Soc.
Release Date : 1971
Mixing Sequences Of Random Variables And Probabilistic Number Theory written by Walter Philipp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Additive functions categories.
The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Diophantine approximations; discrepancies of sequences uniformly distributed mod one and the distribution of additive functions. In addition to new results, the major contribution of the work is the unification of the listed branches of probabilistic number theory. In particular, this is the first time that the distribution theory of additive functions has been related to metric number theory.
Convergence Of Probability Measures
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Author : Patrick Billingsley
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-25
Convergence Of Probability Measures written by Patrick Billingsley and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-25 with Mathematics categories.
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the "industrial-strength" literature available today.
Proceedings Of The International Conference On Number Theory Moscow September 14 18 1971
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Author : Ivan Matveevich Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Proceedings Of The International Conference On Number Theory Moscow September 14 18 1971 written by Ivan Matveevich Vinogradov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Papers and articles about number theory.
Number Theoretic Analysis
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Author : Edmund Hlawka
language : en
Publisher: Springer
Release Date : 2006-11-14
Number Theoretic Analysis written by Edmund Hlawka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Proceedings Of The Sixth Berkeley Symposium On Mathematical Statistics And Probability
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Author : Lucien Marie Le Cam
language : en
Publisher: Univ of California Press
Release Date : 1972
Proceedings Of The Sixth Berkeley Symposium On Mathematical Statistics And Probability written by Lucien Marie Le Cam and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Biometry categories.
The Theory Of Arithmetic Functions
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Author : Anthony A. Gioia
language : en
Publisher: Springer
Release Date : 2006-11-15
The Theory Of Arithmetic Functions written by Anthony A. Gioia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Continued Fractions
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Author : A. M. Rockett
language : en
Publisher: World Scientific
Release Date : 1992-08-01
Continued Fractions written by A. M. Rockett and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-01 with Mathematics categories.
This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Representations Of Real Numbers By Infinite Series
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Author : Janos Galambos
language : en
Publisher: Springer
Release Date : 2006-11-14
Representations Of Real Numbers By Infinite Series written by Janos Galambos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Functional Gaussian Approximation For Dependent Structures
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Author : Florence Merlevède
language : en
Publisher: Oxford University Press
Release Date : 2019-02-14
Functional Gaussian Approximation For Dependent Structures written by Florence Merlevède and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-14 with Mathematics categories.
Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.
The Metrical Theory Of Jacobi Perron Algorithm
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Author : F. Schweiger
language : en
Publisher: Springer
Release Date : 2006-11-15
The Metrical Theory Of Jacobi Perron Algorithm written by F. Schweiger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.