A course in stochastic processes. Stochastic models and statistical inference
type: Item
instance of: scholarly article
title: A course in stochastic processes. Stochastic models and statistical inference
zbMATH Open document ID: 0874.62094
author: Denis Bosq
author: Hung T. Nguyen
published in: Theory and Decision Library. Series B: Mathematical and Statistical Methods
publication date: 1997-07-21T00:00:00Z
review text: This is an elementary introduction to stochastic processes with an initiation to their statistical inference. The material is standard and classical for one-semester courses at graduate level to students of mathematics, statistics, computer science, electrical and industrial engineering, and economics. Measure theory is not required but, whenever necessary, measure-theoretic results are called upon. There are exercises at the end of each chapter with partial solutions. Contents : Preface; 1. Basic probability background; 2. Modeling random phenomena, 3. Discrete-time Markov chains; 4. Poisson processes; 5. Continuous-time Markov chains; 6. Random walks, 7. Renewal theory; 8. Queueing theory; 9. Stationary processes; 10. ARMA model; 11. Discrete-time martingales; 12. Brownian Motion and diffusion processes; 13. Statistics for Poisson processes; 14. Statistics of discrete-time stationary processes; 15. Statistics of diffusion processes; Appendix A: Measure and integration; Appendix B: Banach and Hilbert spaces; List of symbols; Bibliography, Partial solutions to selected exercises; Index. In the reviewer's opinion this is a welcome addition to the textbook literature of stochastic processes.
Mathematics Subject Classification ID: 62M02
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 60Jxx
Mathematics Subject Classification ID: 62M05
zbMATH DE Number: 1037257
zbMATH Keywords: random walks
zbMATH Keywords: renewal theory
zbMATH Keywords: queueing theory
zbMATH Keywords: Markov chains
zbMATH Keywords: Poisson processes
zbMATH Keywords: ARMA model
zbMATH Keywords: martingales
zbMATH Keywords: diffusion processes
reviewed by: Marius Iosifescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1037257