Probability and stochastic modeling / / by Vladimir I. Rotar

• Record Nr.: UNINA9910460601603321
• Autore: Rotar Vladimir I.
• Pubbl/distr/stampa: Boca Raton, FL : , : Chapman and Hall/CRC, an imprint of Taylor and Francis, , 2012
• ISBN: 0-429-10963-6; 1-4398-7207-4
• Edizione: [First edition.]
• Descrizione fisica: 1 online resource (504 p.)
• Disciplina: 519.2
• Soggetti: Probabilities; Stochastic models; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Front Cover; Decation; Preface; Contents; Introduction; Chapter 1. Basic Notions; Chapter 2. Independence and Conditional Probability; Chapter 3. Discrete Random Variables; Chapter 4. Generating Functions. Branching Processes. Random Walk Revisited; Chapter 5. Markov Chains; Chapter 6. Continuous Random Variables; Chapter 7. Distributions in the General Case. Simulation; Chapter 8. Moment Generating Functions; Chapter 9. The Central Limit Theorem for Independent Random Variables; Chapter 10. Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem; Chapter 11. Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival ProbabilitiesChapter 12. Stochastic Processes: Preliminaries; Chapter 13. Counting and Queuing Processes. Birth and Death Processes: A General Scheme; Chapter 14. Elements of Renewal Theory; Chapter 15. Martingales in Discrete Time; Chapter 16. Brownian Motion and Martingales in Continuous Time; Chapter 17. More on Dependency Structures; Chapter 18. Comparison of Random Variables. Risk Evaluation; Appendix. Tables. Some Facts from Calculus and the Theory of Interest; References; Answers to Exercises
• Sommario/riassunto: A First Course in Probability with an Emphasis on Stochastic ModelingProbability 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.