Introduction To Probability Theory: A First Course On The Measure-theoretic Approach (World Scientific Series On Probability Theory And Its Applications)
Author: Nima Moshayedi (Author)
Publisher finelybook 出版社: WSPC
Publication Date 出版日期: 2022-03-20
Language 语言: English
Print Length 页数: 292
ISBN-10: 9811246742
ISBN-13: 9789811246746
Book Description
This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economics, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it. The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part.
Contents:
Cover
FRONT MATTER
Part I. The Modern Probability
Language
Chapter 1 Elements of Combinatorial
Analysis and Simple Random Walks
Chapter 2 The Modern Probability
Language
Part Il. Conditional Expectations.
Martingales and Markov Chains
Chapter 3 Conditional Expectations
Chapter 4 Martingales
Chapter 5 Markov Chains
Appendices
BibliographyAmazon page
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