Book description
An easily accessible, realworld approach to probability and stochastic processes
Introduction to Probability and Stochastic Processes with Applications presents a clear, easytounderstand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous realworld examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena.
The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itô integrals, martingales, and sigma algebras. Additional topical coverage includes:
Distributions of discrete and continuous random variables frequently used in applications
Random vectors, conditional probability, expectation, and multivariate normal distributions
The laws of large numbers, limit theorems, and convergence of sequences of random variables
Stochastic processes and related applications, particularly in queueing systems
Financial mathematics, including pricing methods such as riskneutral valuation and the BlackScholes formula
Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upperundergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.
Table of contents
 Coverpage
 Titlepage
 Copyright
 Dedication
 Contents in Brief
 Contents
 Foreword
 Preface
 Acknowledgments
 Introduction
 1 Basic Concepts
 2 Random Variables and Their Distributions
 3 Some Discrete Distributions
 4 Some Continuous Distributions

5 Random Vectors
 5.1 Joint Distribution of Random Variables
 5.2 Independent Random Variables
 5.3 Distribution of Functions of a Random Vector
 5.4 Covariance and Correlation Coefficient
 5.5 Expected Value of a Random Vector and VarianceCovariance Matrix
 5.6 Joint Probability Generating, Moment Generating and Characteristic Functions
 6 Conditional Expectation
 7 Multivariate Normal Distributions
 8 Limit Theorems
 9 Introduction to Stochastic Processes
 10 Introduction to Queueing Models
 11 Stochastic Calculus
 12 Introduction to Mathematical Finance
 Appendix A: Basic Concepts on Set Theory
 Appendix B: Introduction to Combinatorics
 Appendix C: Topics on Linear Algebra
 Appendix D: Statistical Tables
 Selected Problem Solutions
 References
 Glossary
 Index
Product information
 Title: Introduction to Probability and Stochastic Processes with Applications
 Author(s):
 Release date: June 2012
 Publisher(s): Wiley
 ISBN: 9781118294406
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