An Introduction to Measure-Theoretic Probability Books

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An Introduction to Measure theoretic Probability


An Introduction to Measure theoretic Probability
  • Author : George G. Roussas
  • Publisher : Gulf Professional Publishing
  • Release : 2005
  • ISBN : 9780125990226
  • Language : En, Es, Fr & De
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This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail. * Excellent exposition marked by a clear, coherent and logical devleopment of the subject * Easy to understand, detailed discussion of material * Complete proofs

A User s Guide to Measure Theoretic Probability


A User s Guide to Measure Theoretic Probability
  • Author : David Pollard
  • Publisher : Cambridge University Press
  • Release : 2002
  • ISBN : 0521002893
  • Language : En, Es, Fr & De
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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.

An Introduction to Econometric Theory


An Introduction to Econometric Theory
  • Author : A. Ronald Gallant
  • Publisher : Princeton University Press
  • Release : 2018-06-05
  • ISBN : 9780691186238
  • Language : En, Es, Fr & De
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Intended primarily to prepare first-year graduate students for their ongoing work in econometrics, economic theory, and finance, this innovative book presents the fundamental concepts of theoretical econometrics, from measure-theoretic probability to statistics. A. Ronald Gallant covers these topics at an introductory level and develops the ideas to the point where they can be applied. He thereby provides the reader not only with a basic grasp of the key empirical tools but with sound intuition as well. In addition to covering the basic tools of empirical work in economics and finance, Gallant devotes particular attention to motivating ideas and presenting them as the solution to practical problems. For example, he presents correlation, regression, and conditional expectation as a means of obtaining the best approximation of one random variable by some function of another. He considers linear, polynomial, and unrestricted functions, and leads the reader to the notion of conditioning on a sigma-algebra as a means for finding the unrestricted solution. The reader thus gains an understanding of the relationships among linear, polynomial, and unrestricted solutions. Proofs of results are presented when the proof itself aids understanding or when the proof technique has practical value. A major text-treatise by one of the leading scholars in this field, An Introduction to Econometric Theory will prove valuable not only to graduate students but also to all economists, statisticians, and finance professionals interested in the ideas and implications of theoretical econometrics.

A First Look at Rigorous Probability Theory


A First Look at Rigorous Probability Theory
  • Author : Jeffrey Seth Rosenthal
  • Publisher : World Scientific
  • Release : 2006
  • ISBN : 9789812703705
  • Language : En, Es, Fr & De
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Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.

An Introduction to Measure and Probability


An Introduction to Measure and Probability
  • Author : J.C. Taylor
  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • ISBN : 9781461206590
  • Language : En, Es, Fr & De
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Assuming only calculus and linear algebra, Professor Taylor introduces readers to measure theory and probability, discrete martingales, and weak convergence. This is a technically complete, self-contained and rigorous approach that helps the reader to develop basic skills in analysis and probability. Students of pure mathematics and statistics can thus expect to acquire a sound introduction to basic measure theory and probability, while readers with a background in finance, business, or engineering will gain a technical understanding of discrete martingales in the equivalent of one semester. J. C. Taylor is the author of numerous articles on potential theory, both probabilistic and analytic, and is particularly interested in the potential theory of symmetric spaces.