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 Ito 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.
Content:
Chapter 1 Basic Concepts (pages 1โ49):
Chapter 2 Random Variables and Their Distributions (pages 51โ113):
Chapter 3 Some Discrete Distributions (pages 115โ144):
Chapter 4 Some Continuous Distributions (pages 145โ189):
Chapter 5 Random Vectors (pages 191โ263):
Chapter 6 Conditional Expectation (pages 265โ293):
Chapter 7 Multivariate Normal Distributions (pages 295โ311):
Chapter 8 Limit Theorems (pages 313โ338):
Chapter 9 Introduction to Stochastic Processes (pages 339โ415):
Chapter 10 Introduction to Queueing Models (pages 417โ459):
Chapter 11 Stochastic Calculus (pages 461โ495):
Chapter 12 Introduction to Mathematical Finance (pages 497โ531):