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Mixed Sequences Of Random Variables And Probabilistic Number Theory
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Book Synopsis Mixing Sequences of Random Variables and Probabilistic Number Theory by : Walter Philipp
Download or read book Mixing Sequences of Random Variables and Probabilistic Number Theory written by Walter Philipp and published by American Mathematical Soc.. This book was released on 1971 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mixed sequences of random variables and probabilistic number theory by : Walter Philipp
Download or read book Mixed sequences of random variables and probabilistic number theory written by Walter Philipp and published by . This book was released on 1971 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mixing Sequences of Random Variables and Probabilistic Number Theory by :
Download or read book Mixing Sequences of Random Variables and Probabilistic Number Theory written by and published by . This book was released on 1971-01-30 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probabilistic Number Theory I by : P.D.T.A. Elliott
Download or read book Probabilistic Number Theory I written by P.D.T.A. Elliott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1791 Gauss made the following assertions (collected works, Vol. 10, p.ll, Teubner, Leipzig 1917): Primzahlen unter a (= 00) a la Zahlen aus zwei Factoren lla· a la (warsch.) aus 3 Factoren 1 (lla)2a -- 2 la et sic in info In more modern notation, let 1tk(X) denote the number of integers not exceeding x which are made up of k distinct prime factors, k = 1, 2 ... Then his assertions amount to the asymptotic estimate x (log log X)k-l () 1tk X '"--"';"'-"--"::--:-'-, - (x-..oo). log x (k-1)! The case k = 1, known as the Prime Number Theorem, was independently established by Hadamard and de la Vallee Poussin in 1896, just over a hundred years later. The general case was deduced by Landau in 1900; it needs only an integration by parts. Nevertheless, one can scarcely say that Probabilistic Number Theory began with Gauss. In 1914 the Indian original mathematician Srinivasa Ramanujan arrived in England. Six years of his short life remained to him during which he wrote, amongst other things, five papers and two notes jointly with G.H. Hardy
Book Synopsis Probabilistic Number Theory II by : P.D.T.A. Elliott
Download or read book Probabilistic Number Theory II written by P.D.T.A. Elliott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume we study the value distribution of arithmetic functions, allowing unbounded renormalisations. The methods involve a synthesis of Probability and Number Theory; sums of independent infinitesimal random variables playing an important role. A central problem is to decide when an additive arithmetic function fin) admits a renormalisation by real functions a(x) and {3(x) > 0 so that asx ~ 00 the frequencies vx(n;f (n) - a(x) :s;; z {3 (x) ) converge weakly; (see Notation). In contrast to volume one we allow {3(x) to become unbounded with x. In particular, we investigate to what extent one can simulate the behaviour of additive arithmetic functions by that of sums of suit ably defined independent random variables. This fruiful point of view was intro duced in a 1939 paper of Erdos and Kac. We obtain their (now classical) result in Chapter 12. Subsequent methods involve both Fourier analysis on the line, and the appli cation of Dirichlet series. Many additional topics are considered. We mention only: a problem of Hardy and Ramanujan; local properties of additive arithmetic functions; the rate of convergence of certain arithmetic frequencies to the normal law; the arithmetic simulation of all stable laws. As in Volume I the historical background of various results is discussed, forming an integral part of the text. In Chapters 12 and 19 these considerations are quite extensive, and an author often speaks for himself.
Book Synopsis Sequences, Discrepancies and Applications by : Michael Drmota
Download or read book Sequences, Discrepancies and Applications written by Michael Drmota and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Book Synopsis Almost Sure Invariance Principles for Partial Sums of Weakly Dependent Random Variables by : Walter Philipp
Download or read book Almost Sure Invariance Principles for Partial Sums of Weakly Dependent Random Variables written by Walter Philipp and published by American Mathematical Soc.. This book was released on 1975 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: A strong revival of interest in the law of the iterated logarithm and related asymptotic fluctuation results has occurred in the last decade, stimulated by two remarkable papers by Volker Strassen. In these papers, Strassen introduces a new method for establishing such fluctuation results for sums of independent random variables and for martingales. Strassen's almost sure invariance principle for martingales states that each martingale satisfying a certain second moment condition is with probability on "close" to a Brownian motion. In this monograph we investigate the asymptotic fluctuation behavior of sums of weakly dependent random variables, such as lacunary trigonometric mixing, and Gaussian sequences.
Book Synopsis Empirical Process Techniques for Dependent Data by : Herold Dehling
Download or read book Empirical Process Techniques for Dependent Data written by Herold Dehling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,
Book Synopsis Convergence of Probability Measures by : Patrick Billingsley
Download or read book Convergence of Probability Measures written by Patrick Billingsley and published by John Wiley & Sons. This book was released on 2013-06-25 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings of the International Conference on Number Theory (Moscow, September 14-18, 1971) by : Ivan Matveevich Vinogradov
Download or read book Proceedings of the International Conference on Number Theory (Moscow, September 14-18, 1971) written by Ivan Matveevich Vinogradov and published by American Mathematical Soc.. This book was released on 1975 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers and articles about number theory.
Book Synopsis An Introduction to Probabilistic Number Theory by : Emmanuel Kowalski
Download or read book An Introduction to Probabilistic Number Theory written by Emmanuel Kowalski and published by Cambridge University Press. This book was released on 2021-05-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
Book Synopsis Number-Theoretic Analysis by : Edmund Hlawka
Download or read book Number-Theoretic Analysis written by Edmund Hlawka and published by Springer. This book was released on 2006-11-14 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Arithmetic Functions by : Anthony A. Gioia
Download or read book The Theory of Arithmetic Functions written by Anthony A. Gioia and published by Springer. This book was released on 2006-11-15 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability by : Lucien Marie Le Cam
Download or read book Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability written by Lucien Marie Le Cam and published by Univ of California Press. This book was released on 1972 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limit Theorems of Probability Theory by : Yu.V. Prokhorov
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
Book Synopsis Representations of Real Numbers by Infinite Series by : Janos Galambos
Download or read book Representations of Real Numbers by Infinite Series written by Janos Galambos and published by Springer. This book was released on 2006-11-14 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Library of Congress. Copyright Office Publisher :Copyright Office, Library of Congress ISBN 13 : Total Pages :1040 pages Book Rating :4.F/5 ( download)
Book Synopsis Catalog of Copyright Entries. Third Series by : Library of Congress. Copyright Office
Download or read book Catalog of Copyright Entries. Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1973 with total page 1040 pages. Available in PDF, EPUB and Kindle. Book excerpt: