Download or read book The Life and Times of the Central Limit Theorem written by William J. Adams and published by American Mathematical Soc.. This book was released on 2009-11-25 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the First Edition: The study of any topic becomes more meaningful if one also studies the historical development that resulted in the final theorem. ... This is an excellent book on mathematics in the making. --Philip Peak, The Mathematics Teacher, May, 1975 I find the book very interesting. It contains valuable information and useful references. It can be recommended not only to historians of science and mathematics but also to students of probability and statistics. --Wei-Ching Chang, Historica Mathematica, August, 1976 In the months since I wrote ... I have read it from cover to cover at least once and perused it here and there a number of times. I still find it a very interesting and worthwhile contribution to the history of probability and statistics. --Churchill Eisenhart, past president of the American Statistical Association, in a letter to the author, February 3, 1975 The name Central Limit Theorem covers a wide variety of results involving the determination of necessary and sufficient conditions under which sums of independent random variables, suitably standardized, have cumulative distribution functions close to the Gaussian distribution. As the name Central Limit Theorem suggests, it is a centerpiece of probability theory which also carries over to statistics. Part One of The Life and Times of the Central Limit Theorem, Second Edition traces its fascinating history from seeds sown by Jacob Bernoulli to use of integrals of $\exp (x^2)$ as an approximation tool, the development of the theory of errors of observation, problems in mathematical astronomy, the emergence of the hypothesis of elementary errors, the fundamental work of Laplace, and the emergence of an abstract Central Limit Theorem through the work of Chebyshev, Markov and Lyapunov. This closes the classical period of the life of the Central Limit Theorem, 1713-1901. The second part of the book includes papers by Feller and Le Cam, as well as comments by Doob, Trotter, and Pollard, describing the modern history of the Central Limit Theorem (1920-1937), in particular through contributions of Lindeberg, Cramer, Levy, and Feller. The Appendix to the book contains four fundamental papers by Lyapunov on the Central Limit Theorem, made available in English for the first time.
Download or read book Martingale Limit Theory written by Peter Gavin Hall and published by . This book was released on 1975 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
Download or read book Some Remarks on the Martingale Central Limit Theorem written by Esbjörn Ohlsson and published by . This book was released on 1985 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Martingale Approximation written by Yu. V. Borovskikh and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-01-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Martingale Approximation".
Download or read book Sequential Estimation written by Malay Ghosh and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only comprehensive guide to the theory and practice of one oftoday's most important probabilistic techniques The past 15 years have witnessed many significant advances insequential estimation, especially in the areas of three-stage andnonparametric methodology. Yet, until now, there were no referencesdevoted exclusively to this rapidly growing statisticalfield. Sequential Estimation is the first, single-source guide to thetheory and practice of both classical and modern sequentialestimation techniques--including parametric and nonparametricmethods. Researchers in sequential analysis will appreciate theunified, logically integrated treatment of the subject, as well ascoverage of important contemporary procedures not covered in moregeneral sequential analysis texts, such as: * Shrinkage estimation * Empirical and hierarchical Bayes procedures * Multistage sampling and accelerated sampling procedures * Time-sequential estimation * Sequential estimation in finite population sampling * Reliability estimation and capture-recapture methodologiesleading to sequential tagging schemes An indispensable resource for researchers in sequential analysis,Sequential Estimation is an ideal graduate-level text as well.
Download or read book Ergodic Behavior of Markov Processes written by Alexei Kulik and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems
Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.
Download or read book Stochastic Dynamics Filtering and Optimization written by Debasish Roy and published by Cambridge University Press. This book was released on 2017-05-04 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces essential concepts in stochastic processes that interface seamlessly with applications of interest in science and engineering.
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Download or read book Probability and Finance written by Glenn Shafer and published by John Wiley & Sons. This book was released on 2005-02-25 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.
Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2006-05-10 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L=82vy processes, weak convergence, It=93 calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales. Though primarily intended as a general reference for researchers and graduate students in probability theory and related areas of analysis, the book is also suitable as a text for graduate and seminar courses on all levels, from elementary to advanced. Numerous easy to more challenging exercises are provided, especially for the early chapters. From the author of "Random Measures".
Download or read book Econometric Modelling with Time Series written by Vance Martin and published by Cambridge University Press. This book was released on 2013 with total page 925 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Download or read book Recent Results in Estimation Theory and Related Topics written by Edward J. Dudewicz and published by . This book was released on 1984 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Splendors and Miseries of Martingales written by Laurent Mazliak and published by Springer Nature. This book was released on 2022-10-17 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler’s holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.
Download or read book A User s Guide to Measure Theoretic Probability written by David Pollard and published by Cambridge University Press. This book was released on 2002 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
Download or read book Probability Theory written by Lucien Marie Le Cam and published by Univ of California Press. This book was released on 1972 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:
