Probability and Stochastic Modeling
Purchasing Options
Features
- Examines modern tendencies in probability theory
- Discusses key current topics not usually addressed in introductory courses
- Describes important stochastic models
- Includes examples and exercises on numerical calculations using Excel
- Presents practical aspects and restrictions of approaches
- Allows instructors to easily construct various courses at different levels of difficulty and with different goals
Solutions manual available for qualifying instructors
Summary
With a focus on applications, this unique introductory book goes beyond the standard facts typically presented in probability texts. It includes a variety of stochastic models of real phenomena and methods of modeling, such as simulation, Markov chains, counting and compound processes, simple trees, queuing theory, reliability models, diffusion, and models of the financial market. It contains numerous examples from various fields, including economics, finance, insurance, computer science, and physics. The text also provides examples and exercises on numerical calculations using Excel.
Table of Contents
Probability Space: Sample Space, Events, Probability. Independence and Conditional Probabilities. Discrete Random Variables. Generating Functions. The Extinction Problem. Random Walk Revisited. More about Markov Chains. Continuous r.v.'s. Distributions and Expectations in the General Case. Simulation and the Monte Carlo Method. Moment Generating Functions. The Bernstein-Chernoff Bounds. Covariance Analysis and Multivariate Normal Distribution. Some Markov Stochastic Processes and Stochastic Dynamic Models of Real Phenomena. Martingales. Some Other Types of Dependencies. Dependencies Not Connected with Evolution in Time. The Central Limit Theorem. Reliability Models and Renewal Processes. Risk Assessment and Comparison of r.v.'s. Brownian Motion. Almost Sure Behavior of Sums of r.v.'s. Appendix. References. Answers to Exercises. Index.
Editorial Reviews
This is a superbly written text on probability and stochastic processes for students who have had two semesters of calculus and an introductory course in linear algebra. This includes upper division students in science and engineering including statistics and mathematics, as well as students in fields such as economics and finance. In addition, it will be a wonderful book for self study for many others. Important and well-chosen examples illustrate the theory throughout, and a large body of exercises supplements the text. It gives a lucid presentation of basic probability theory, including Markov chains and martingales. A special feature of this book is a marvelous exposition of many interesting aspects of financial mathematics that are generally considered rather intricate and inaccessible at this level. One will find here enlightening discussions and some central results on arbitrage and derivatives, and pricing of American and European options. This book carries the imprint of a distinguished mathematician and teacher with expertise in probability theory and many of its special applications to mathematical economics and finance. It is an outstanding addition to the field requiring only a modest background in mathematics.
—Rabi Bhattacharya, Department of Mathematics, University of Arizona
Written in a lively and stimulating manner, the book makes a very good impression. The author, having extensive teaching experience and an undoubted literary talent, has managed to create an original introduction to modern probability theory. The successful combination of a variety of examples, exercises and applications with deep and nontrivial ideas makes the book interesting not only for beginning students, but also for professionals working with probabilistic problems. I believe that the book can serve as an ideal textbook for anyone interested in probability theory and its applications. The book will take a worthy place in the literature on probabilistic issues.
—Davydov Youri, Laboratoire Paul Painlevé, Université des Sciences et Technologies de Lille, France