This book offers a concise introduction to some of the stochastic processes that frequently arise in applied probability. Emphasis is on optimization models and methods, particularly in the area of decision processes. After reviewing some basic notions of probability theory and stochastic processes, the author presents a useful treatment of the Poisson process, including compound and nonhomogeneous Poisson processes. Subsequent chapters deal with such topics as renewal theory and Markov chains; semi-Markov, Markov renewal, and regenerative processes; inventory theory; and Brownian motion and continuous time optimization models.
Each chapter is followed by a section of useful problems that illustrate and complement the text. There is also a short list of relevant references at the end of every chapter. Students will find this a largely self-contained text that requires little previous knowledge of the subject. It is especially suited for a one-year course in applied probability at the advanced undergraduate or beginning postgraduate level. 1970 edition.
The hallmark features of this text have been retained in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. The book contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams. It also presents new applications of probability models in biology and new material on Point Processes, including the Hawkes process. There is a list of commonly used notations and equations, along with an instructor's solutions manual.
This text will be a helpful resource for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.Updated data, and a list of commonly used notations and equations, instructor's solutions manualOffers new applications of probability models in biology and new material on Point Processes, including the Hawkes processIntroduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations researchCovers finite capacity queues, insurance risk models, and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new examsAppropriate for a full year course, this book is written under the assumption that students are familiar with calculus
To help guide students towards independent learning, exercises and examples using real issues and real data (e.g., stock price models, health issues, gender issues, sports, scientific fraud) are provided. The chapters end with detailed reviews of important concepts and formulas, key terms, and definitions that are useful study tools. Data sets from text and exercise material are available for download in the text website.
This text is designed for introductory non-calculus based statistics courses that are offered by mathematics and/or statistics departments to undergraduate students taking a semester course in basic Statistics or a year course in Probability and Statistics.Unique historical perspective profiling prominent statisticians and historical events to motivate learning by providing interest and contextUse of exercises and examples helps guide the student towards indpendent learning using real issues and real data, e.g. stock price models, health issues, gender issues, sports, scientific fraud. Summary/Key Terms- chapters end with detailed reviews of important concepts and formulas, key terms and definitions which are useful to students as study tools
As with the previous editions, Ross' text has remendously clear exposition, plus real-data examples and exercises throughout the text. Numerous exercises, examples, and applications
apply probability theory to everyday statistical problems and situations.
New to the 4th Edition:
- New Chapter on Simulation, Bootstrap Statistical Methods, and Permutation Tests
- 20% New Updated problem sets and applications, that demonstrate updated applications to engineering as well as biological, physical and computer science
- New Real data examples that use significant real data from actual studies across life science, engineering, computing and business
- New End of Chapter review material that emphasizes key ideas as well as the risks associated with practical application of the material
This latest edition features all-new material on variance reduction, including control variables and their use in estimating the expected return at blackjack and their relation to regression analysis. Additionally, the 5th edition expands on Markov chain monte carlo methods, and offers unique information on the alias method for generating discrete random variables.
By explaining how a computer can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time, Ross’s Simulation, 5th edition presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.Additional material on variance reduction, including control variables and their use in estimating the expected return at blackjack and their relation to regression analysisAdditional material and examples on Markov chain Monte Carlo methodsUnique material on the alias method for generating discrete random variablesAdditional material on generating multivariate normal vectors
The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented.
The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.