A Graduate Course in Probability
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A Graduate Course in Probability

SKU: 9781483220505

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Full Title

A Graduate Course in Probability
Author(s)

Howard G. Tucker
Edition
ISBN

9781483220505, 9780127026466
Publisher

Academic Press
Format

PDF and EPUB

Description

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini’s theorem, Radon-Nikodym theorem, Egorov’s theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work.

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A Graduate Course in Probability
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Availability: In Stock

A Graduate Course in Probability

SKU: 9780486782119

Original price was: $16.95.Current price is: $4.24.

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Additional information

Full Title

A Graduate Course in Probability
Author(s)

Howard G. Tucker
Edition
ISBN

9780486782119, 9780486493039
Publisher

Dover Publications
Format

PDF and EPUB

Description

Suitable for a graduate course in analytic probability theory, this text requires no previous knowledge of probability and only a limited background in real analysis. In addition to providing instruction for graduate students in mathematics and mathematical statistics, the book features detailed proofs that offer direct access to the basic theorems of probability theory for mathematicians of all interests. The treatment strikes a balance between measure-theoretic aspects of probability and distribution aspects, presenting some of the basic theorems of analytic probability theory in a cohesive manner. Statements are rendered as simply as possible in order to make them easy to remember and to demonstrate the essential idea behind each proof. Topics include probability spaces and distributions, stochastic independence, basic limiting operations, strong limit theorems for independent random variables, the central limit theorem, conditional expectation and Martingale theory, and an introduction to stochastic processes, particularly Brownian motion. Each section concludes with problems that reinforce the preceding material.

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A Graduate Course in Probability
-70%
Availability: In Stock

A Graduate Course in Probability

SKU: 9789811255106

Original price was: $39.90.Current price is: $11.97.

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Full Title

A Graduate Course in Probability
Author(s)

Liviu I Nicolaescu
Edition
ISBN

9789811255106, 9789811255083, 9789811255090
Publisher

WSPC
Format

PDF and EPUB

Description

This book grew out of the notes for a one-semester basic graduate course in probability. As the title suggests, it is meant to be an introduction to probability and could serve as textbook for a year long text for a basic graduate course. It assumes some familiarity with measure theory and integration so in this book we emphasize only those aspects of measure theory that have special probabilistic uses.The book covers the topics that are part of the culture of an aspiring probabilist and it is guided by the author’s personal belief that probability was and is a theory driven by examples. The examples form the main attraction of this subject. For this reason, a large book is devoted to an eclectic collection of examples, from classical to modern, from mainstream to “exotic”. The text is complemented by nearly 200 exercises, quite a few nontrivial, but all meant to enhance comprehension and enlarge the reader’s horizons.While teaching probability both at undergraduate and graduate level the author discovered the revealing power of simulations. For this reason, the book contains a veiled invitation to the reader to familiarize with the programing language R. In the appendix, there are a few of the most frequently used operations and the text is sprinkled with (less than optimal) R codes. Nowadays one can do on a laptop simulations and computations we could only dream as an undergraduate in the past. This is a book written by a probability outsider. That brings along a bit of freshness together with certain “naiveties”.

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