A course in stochastic processes. Stochastic models and statistical inference
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.
scientific article; zbMATH DE number 1037257