Introduction to Probability and Measure Book

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Introduction to Probability and Measure

By K.R. Parthasarathy
  • ISBN Code: : 9386279274
  • Publisher : Springer
  • Pages : 354
  • Category : Mathematics
  • Reads : 446
  • Book Compatibility : Pdf, ePub, Mobi, Kindle
  • Pdf : introduction-to-probability-and-measure.pdf

Book Excerpt :

According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account.

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Book Short Summary:

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Book Short Summary:

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Book Short Summary:

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Book Short Summary:

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  • Total of Pages : 608
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  • Pdf File: probability.pdf

Book Short Summary:

This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.

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  • Publisher : Springer Science & Business Media
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  • Pdf File: measure-integral-and-probability.pdf

Book Short Summary:

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

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This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

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  • Total of Pages : 312
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  • Pdf File: lebesgue-measure-and-integration.pdf

Book Short Summary:

A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration. Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.

Introduction to Statistics and Data Analysis

By Christian Heumann,Michael Schomaker,Shalabh
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer
  • Book Code : 3319461621
  • Total of Pages : 456
  • Category : Mathematics
  • Members : 742
  • Pdf File: introduction-to-statistics-and-data-analysis.pdf

Book Short Summary:

This introductory statistics textbook conveys the essential concepts and tools needed to develop and nurture statistical thinking. It presents descriptive, inductive and explorative statistical methods and guides the reader through the process of quantitative data analysis. In the experimental sciences and interdisciplinary research, data analysis has become an integral part of any scientific study. Issues such as judging the credibility of data, analyzing the data, evaluating the reliability of the obtained results and finally drawing the correct and appropriate conclusions from the results are vital. The text is primarily intended for undergraduate students in disciplines like business administration, the social sciences, medicine, politics, macroeconomics, etc. It features a wealth of examples, exercises and solutions with computer code in the statistical programming language R as well as supplementary material that will enable the reader to quickly adapt all methods to their own applications.

Measure, Probability, and Mathematical Finance

By Guojun Gan,Chaoqun Ma,Hong Xie
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : John Wiley & Sons
  • Book Code : 1118831985
  • Total of Pages : 744
  • Category : Mathematics
  • Members : 916
  • Pdf File: measure-probability-and-mathematical-finance.pdf

Book Short Summary:

An introduction to the mathematical theory and financialmodels developed and used on Wall Street Providing both a theoretical and practical approach to theunderlying mathematical theory behind financial models, Measure,Probability, and Mathematical Finance: A Problem-OrientedApproach presents important concepts and results in measuretheory, probability theory, stochastic processes, and stochasticcalculus. Measure theory is indispensable to the rigorousdevelopment of probability theory and is also necessary to properlyaddress martingale measures, the change of numeraire theory, andLIBOR market models. In addition, probability theory is presentedto facilitate the development of stochastic processes, includingmartingales and Brownian motions, while stochastic processes andstochastic calculus are discussed to model asset prices and developderivative pricing models. The authors promote a problem-solving approach when applyingmathematics in real-world situations, and readers are encouraged toaddress theorems and problems with mathematical rigor. In addition,Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measuretheory, probability theory, stochastic processes, and stochasticcalculus Over 500 problems with hints and select solutions to reinforcebasic concepts and important theorems Classic derivative pricing models in mathematical finance thathave been developed and published since the seminal work of Blackand Scholes Measure, Probability, and Mathematical Finance: AProblem-Oriented Approach is an ideal textbook for introductoryquantitative courses in business, economics, and mathematicalfinance at the upper-undergraduate and graduate levels. The book isalso a useful reference for readers who need to build theirmathematical skills in order to better understand the mathematicaltheory of derivative pricing models.

A Course in Probability Theory

By Kai Lai Chung
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Elsevier
  • Book Code : 008052298X
  • Total of Pages : 419
  • Category : Mathematics
  • Members : 566
  • Pdf File: a-course-in-probability-theory.pdf

Book Short Summary:

Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

A Logical Introduction to Probability and Induction

By Franz Huber
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Oxford University Press
  • Book Code : 0190845414
  • Total of Pages : 256
  • Category : Mathematics
  • Members : 119
  • Pdf File: a-logical-introduction-to-probability-and-induction.pdf

Book Short Summary:

A Logical Introduction to Probability and Induction is a textbook on the mathematics of the probability calculus and its applications in philosophy. On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of the probability calculus. On the philosophical side, the main focus is on the problem of induction and its reception in epistemology and the philosophy of science. Particular emphasis is placed on the means-end approach to the justification of inductive inference rules. In addition, the book discusses the major interpretations of probability. These are philosophical accounts of the nature of probability that interpret the mathematical structure of the probability calculus. Besides the classical and logical interpretation, they include the interpretation of probability as chance, degree of belief, and relative frequency. The Bayesian interpretation of probability as degree of belief locates probability in a subject's mind. It raises the question why her degrees of belief ought to obey the probability calculus. In contrast to this, chance and relative frequency belong to the external world. While chance is postulated by theory, relative frequencies can be observed empirically. A Logical Introduction to Probability and Induction aims to equip students with the ability to successfully carry out arguments. It begins with elementary deductive logic and uses it as basis for the material on probability and induction. Throughout the textbook results are carefully proved using the inference rules introduced at the beginning, and students are asked to solve problems in the form of 50 exercises. An instructor's manual contains the solutions to these exercises as well as suggested exam questions. The book does not presuppose any background in mathematics, although sections 10.3-10.9 on statistics are technically sophisticated and optional. The textbook is suitable for lower level undergraduate courses in philosophy and logic.

A Natural Introduction to Probability Theory

By Ronald Meester
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Birkhäuser
  • Book Code : 3034877862
  • Total of Pages : 192
  • Category : Mathematics
  • Members : 289
  • Pdf File: a-natural-introduction-to-probability-theory.pdf

Book Short Summary:

Compactly written, but nevertheless very readable, appealing to intuition, this introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Technical machinery is only introduced when necessary. The route is rigorous but does not use measure theory. The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory. Only first-year calculus is required.

Measure Theory

By Donald L. Cohn
  • File : Pdf, ePub, Mobi, Kindle
  • Publisher : Springer Science & Business Media
  • Book Code : 1461469562
  • Total of Pages : 457
  • Category : Mathematics
  • Members : 371
  • Pdf File: measure-theory.pdf

Book Short Summary:

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.