## Book Description

An easily accessible, real-world approach to probability and stochastic processes

Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand 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 real-world 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 risk-neutral valuation and the Black-Scholes 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 upper-undergraduate 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.

1. Coverpage
2. Titlepage
4. Dedication
5. Contents in Brief
6. Contents
7. Foreword
8. Preface
9. Acknowledgments
10. Introduction
11. 1 Basic Concepts
1. 1.1 Probability Space
2. 1.2 Laplace Probability Space
3. 1.3 Conditional Probability and Event Independence
4. 1.4 Geometric Probability
12. 2 Random Variables and Their Distributions
13. 3 Some Discrete Distributions
1. 3.1 Discrete Uniform, Binomial and Bernoulli Distributions
2. 3.2 Hypergeometric and Poisson Distributions
3. 3.3 Geometric and Negative Binomial Distributions
14. 4 Some Continuous Distributions
1. 4.1 Uniform Distribution
2. 4.2 Normal Distribution
3. 4.3 Family of Gamma Distributions
4. 4.4 Weibull Distribution
5. 4.5 Beta Distribution
6. 4.6 Other Continuous Distributions
15. 5 Random Vectors
16. 6 Conditional Expectation
1. 6.1 Conditional Distribution
2. 6.2 Conditional Expectation Given a σ-Algebra
17. 7 Multivariate Normal Distributions
1. 7.1 Multivariate Normal Distribution
2. 7.2 Distribution of Quadratic Forms of Multivariate Normal Vectors
18. 8 Limit Theorems
1. 8.1 The Weak Law of Large Numbers
2. 8.2 Convergence of Sequences of Random Variables
3. 8.3 The Strong Law of Large Numbers
4. 8.4 Central Limit Theorem
19. 9 Introduction to Stochastic Processes
1. 9.1 Definitions and Properties
2. 9.2 Discrete-Time Markov Chain
3. 9.3 Continuous-Time Markov Chains
4. 9.4 Poisson Process
5. 9.5 Renewal Processes
6. 9.6 Semi-Markov Process
20. 10 Introduction to Queueing Models
1. 10.1 Introduction
2. 10.2 Markovian Single-Server Models
3. 10.3 Markovian MultiServer Models
4. 10.4 Non-Markovian Models
21. 11 Stochastic Calculus
1. 11.1 Martingales
2. 11.2 Brownian Motion
3. 11.3 Itô Calculus
22. 12 Introduction to Mathematical Finance
1. 12.1 Financial Derivatives
2. 12.2 Discrete-Time Models
3. 12.3 Continuous-Time Models
4. 12.4 Volatility
23. Appendix A: Basic Concepts on Set Theory
24. Appendix B: Introduction to Combinatorics
25. Appendix C: Topics on Linear Algebra
26. Appendix D: Statistical Tables
27. Selected Problem Solutions
28. References
29. Glossary
30. Index

## Product Information

• Title: Introduction to Probability and Stochastic Processes with Applications
• Author(s): Selvamuthu Dharmaraja, Viswanathan Arunachalam, Liliana Blanco Castaneda
• Release date: June 2012
• Publisher(s): Wiley
• ISBN: 9781118294406