Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in "routes" designated by special "roadside" markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study.
Table of Contents
Basic Notions. Independence and Conditional Probability. Discrete Random Variables. Generating Functions. Branching Processes. Random Walk Revisited. Markov Chains. Continuous Random Variables. Distributions in the General Case. Simulation. Moment Generating Functions. The Central Limit Theorem for Independent Random Variables. Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem. Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival Probabilities. Stochastic Processes: Preliminaries. Counting and Queuing Processes. Birth and Death Processes: A General Scheme. Elements of Renewal Theory. Martingales in Discrete Time. Brownian Motion and Martingales in Continuous Time. More on Dependency Structures. Comparison of Random Variables. Risk Evaluation. Appendix. References. Answers to Exercises. Index.
Vladimir I. Rotar is a professor in the Department of Mathematics and Statistics at San Diego State University. Dr. Rotar has authored four books and more than 100 scientific papers on probability theory and its applications in leading mathematical journals.