Introduction to Probability and Stochastic Processes with Applications.
Title:
Introduction to Probability and Stochastic Processes with Applications.
Author:
Blanco Castañeda, Liliana.
ISBN:
9781118344941
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (616 pages)
Contents:
Introduction to Probability and Stochastic Processes with Applications -- CONTENTS -- Foreword -- Preface -- Acknowledgments -- Introduction -- 1 Basic Concepts -- 1.1 Probability Space -- 1.2 Laplace Probability Space -- 1.3 Conditional Probability and Event Independence -- 1.4 Geometric Probability -- Exercises -- 2 Random Variables and Their Distributions -- 2.1 Definitions and Properties -- 2.2 Discrete Random Variables -- 2.3 Continuous Random Variables -- 2.4 Distribution of a Function of a Random Variable -- 2.5 Expected Value and Variance of a Random Variable -- Exercises -- 3 Some Discrete Distributions -- 3.1 Discrete Uniform, Binomial and Bernoulli Distributions -- 3.2 Hypergeometric and Poisson Distributions -- 3.3 Geometric and Negative Binomial Distributions -- Exercises -- 4 Some Continuous Distributions -- 4.1 Uniform Distribution -- 4.2 Normal Distribution -- 4.3 Family of Gamma Distributions -- 4.4 Weibull Distribution -- 4.5 Beta Distribution -- 4.6 Other Continuous Distributions -- Exercises -- 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 Variance-Covariance Matrix -- 5.6 Joint Probability Generating, Moment Generating and Characteristic Functions -- Exercises -- 6 Conditional Expectation -- 6.1 Conditional Distribution -- 6.2 Conditional Expectation Given a σ-Algebra -- Exercises -- 7 Multivariate Normal Distributions -- 7.1 Multivariate Normal Distribution -- 7.2 Distribution of Quadratic Forms of Multivariate Normal Vectors -- Exercises -- 8 Limit Theorems -- 8.1 The Weak Law of Large Numbers -- 8.2 Convergence of Sequences of Random Variables -- 8.3 The Strong Law of Large Numbers -- 8.4 Central Limit Theorem -- Exercises.
9 Introduction to Stochastic Processes -- 9.1 Definitions and Properties -- 9.2 Discrete-Time Markov Chain -- 9.2.1 Classification of States -- 9.2.2 Measure of Stationary Probabilities -- 9.3 Continuous-Time Markov Chains -- 9.4 Poisson Process -- 9.5 Renewal Processes -- 9.6 Semi-Markov Process -- Exercises -- 10 Introduction to Queueing Models -- 10.1 Introduction -- 10.2 Markovian Single-Server Models -- 10.2.1 M/M/l/∞ Queueing System -- 10.2.2 M/M/l/N Queueing System -- 10.3 Markovian MultiServer Models -- 10.3.1 M/M/c/∞ Queueing System -- 10.3.2 M/M/c/c Loss System -- 10.3.3 M/M/c/K Finite-Capacity Queueing System -- 10.3.4 M/M/∞ Queueing System -- 10.4 Non-Markovian Models -- 10.4.1 M/G/l Queueing System -- 10.4.2 GI/M/1 Queueing System -- 10.4.3 M/G/l/N Queueing System -- 10.4.4 GI/M/1/N Queueing System -- Exercises -- 11 Stochastic Calculus -- 11.1 Martingales -- 11.2 Brownian Motion -- 11.3 Itô Calculus -- Exercises -- 12 Introduction to Mathematical Finance -- 12.1 Financial Derivatives -- 12.2 Discrete-Time Models -- 12.2.1 The Binomial Model -- 12.2.2 Multi-Period Binomial Model -- 12.3 Continuous-Time Models -- 12.3.1 Black-Scholes Formula European Call Option -- 12.3.2 Properties of Black-Scholes Formula -- 12.4 Volatility -- Exercises -- Appendix A: Basic Concepts on Set Theory -- Appendix B: Introduction to Combinatorics -- Exercises -- Appendix C: Topics on Linear Algebra -- Appendix D: Statistical Tables -- D.1 Binomial Probabilities -- D.2 Poisson Probabilities -- D.3 Standard Normal Distribution Function -- D.4 Chi-Square Distribution Function -- Selected Problem Solutions -- References -- Glossary -- Index.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Electronic Access:
Click to View