From Classical To Modern Probability

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A History Of The Central Limit Theorem

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Author : Hans Fischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-08

A History Of The Central Limit Theorem written by Hans Fischer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-08 with Mathematics categories.

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.

Probability The Classical Limit Theorems

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Author : Henry McKean
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-27

Probability The Classical Limit Theorems written by Henry McKean and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Computers categories.

A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role.

Foundations Of Modern Probability

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Author : Olav Kallenberg
language : en
Publisher:
Release Date : 2014-01-15

Foundations Of Modern Probability written by Olav Kallenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Creating Modern Probability

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Author : Jan von Plato
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-12

Creating Modern Probability written by Jan von Plato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-12 with Mathematics categories.

In this book the author charts the history and development of modern probability theory.

Classical Probability In The Enlightenment New Edition

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Author : Lorraine Daston
language : en
Publisher: Princeton University Press
Release Date : 2023-08-08

Classical Probability In The Enlightenment New Edition written by Lorraine Daston and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-08 with Science categories.

An award-winning history of the Enlightenment quest to devise a mathematical model of rationality What did it mean to be reasonable in the Age of Reason? Enlightenment mathematicians such as Blaise Pascal, Jakob Bernoulli, and Pierre Simon Laplace sought to answer this question, laboring over a theory of rational decision, action, and belief under conditions of uncertainty. Lorraine Daston brings to life their debates and philosophical arguments, charting the development and application of probability theory by some of the greatest thinkers of the age. Now with an incisive new preface, Classical Probability in the Enlightenment traces the emergence of new kind of mathematics designed to turn good sense into a reasonable calculus.

The Theory Of Probability

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Author : Santosh S. Venkatesh
language : en
Publisher: Cambridge University Press
Release Date : 2013

The Theory Of Probability written by Santosh S. Venkatesh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

From classical foundations to modern theory, this comprehensive guide to probability interweaves mathematical proofs, historical context and detailed illustrative applications.

Theory Of Probability And Random Processes

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Author : Leonid Koralov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-10

Theory Of Probability And Random Processes written by Leonid Koralov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-10 with Mathematics categories.

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

Problems In Probability

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Author : T. M. Mills
language : en
Publisher: World Scientific
Release Date : 2001

Problems In Probability written by T. M. Mills and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Probability theory is an important part of contemporary mathematics. It plays a key role in the insurance industry, in the modelling of financial markets, and in statistics generally ? including all those fields of endeavour to which statistics is applied (e.g. health, physical sciences, engineering, economics). The 20th century has been an important period for the subject, because we have witnessed the development of a solid mathematical basis for the study of probability, especially from the Russian school of probability under the leadership of A N Kolmogorov. We have also seen many new applications of probability ? from applications of stochastic calculus in the financial industry to Internet gambling. At the beginning of the 21st century, the subject offers plenty of scope for theoretical developments, modern applications and computational problems. There is something for everyone in probability The notes and problems in this book have been designed to provide a basis for a series of lectures suitable for advanced undergraduate students on the subject of probability. Through problem solving, students can experience the excitement associated with probability. This activity will help them to develop their problem-solving skills, which are so valuable in today's world. The problems in the book will introduce the student to some famous works and workers in probability and convey the historical, classical and contemporary aspects of probability. A key feature of the book is that many problems are in fact small guided research projects. The research work involved in solving the problems will enhance the student's library research skills.

Introduction To Stochastic Processes

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Author : Mu-fa Chen
language : en
Publisher: World Scientific
Release Date : 2021-05-25

Introduction To Stochastic Processes written by Mu-fa Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-25 with Mathematics categories.

The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.

Probability Theory

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Author : R.G. Laha
language : en
Publisher: Courier Dover Publications
Release Date : 2020-05-21

Probability Theory written by R.G. Laha and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Mathematics categories.

This comprehensive presentation of the basic concepts of probability theory examines both classical and modern methods. The treatment emphasizes the relationship between probability theory and mathematical analysis, and it stresses applications to statistics as well as to analysis. Topics include: • The laws of large numbers • Distribution and characteristic functions • The central limit problem • Dependence • Random variables taking values in a normed linear space Each chapter features worked examples in addition to problems, and bibliographical references to supplementary reading material enhance the text. For advanced undergraduates and graduate students in mathematics.