Ebook: A Course in Stochastic Processes: Stochastic Models and Statistical Inference

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math­ ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti­ vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math­ ematically?". The exercises at the end of each lesson will deepen the stu­ dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.

---

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while at the same time students learn to apply theoretical models.
The lessons cover basic stochastic processes such as Poisson processes, Markov chains, random walks, renewal theory, queuing theory, ARMA models, martingales, Brownian motion and diffusion processes. The statistical topics treated include the basic aspects of statistics of point processes, stationary processes and diffusion processes.
Audience: This textbook will be useful for one-semester courses at graduate level to students of mathematics, statistics, computer science, electrical and industrial engineering and economics.

---

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while at the same time students learn to apply theoretical models.
The lessons cover basic stochastic processes such as Poisson processes, Markov chains, random walks, renewal theory, queuing theory, ARMA models, martingales, Brownian motion and diffusion processes. The statistical topics treated include the basic aspects of statistics of point processes, stationary processes and diffusion processes.
Audience: This textbook will be useful for one-semester courses at graduate level to students of mathematics, statistics, computer science, electrical and industrial engineering and economics.
Content:
Front Matter....Pages i-x
Basic Probability Background....Pages 1-32
Modeling Random Phenomena....Pages 33-44
Discrete — Time Markov Chains....Pages 45-77
Poisson Processes....Pages 79-94
Continuous — Time Markov Chains....Pages 95-116
Random Walks....Pages 117-146
Renewal Theory....Pages 147-169
Queueing Theory....Pages 171-188
Stationary Processes....Pages 189-203
ARMA model....Pages 205-217
Discrete-Time Martingales....Pages 219-232
Brownian Motion and Diffusion Processes....Pages 233-253
Statistics for Poisson Processes....Pages 255-269
Statistics of Discrete-Time Stationary Processes....Pages 271-285
Statistics of Diffusion Processes....Pages 287-298
Back Matter....Pages 299-354

---

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while at the same time students learn to apply theoretical models.
The lessons cover basic stochastic processes such as Poisson processes, Markov chains, random walks, renewal theory, queuing theory, ARMA models, martingales, Brownian motion and diffusion processes. The statistical topics treated include the basic aspects of statistics of point processes, stationary processes and diffusion processes.
Audience: This textbook will be useful for one-semester courses at graduate level to students of mathematics, statistics, computer science, electrical and industrial engineering and economics.
Content:
Front Matter....Pages i-x
Basic Probability Background....Pages 1-32
Modeling Random Phenomena....Pages 33-44
Discrete — Time Markov Chains....Pages 45-77
Poisson Processes....Pages 79-94
Continuous — Time Markov Chains....Pages 95-116
Random Walks....Pages 117-146
Renewal Theory....Pages 147-169
Queueing Theory....Pages 171-188
Stationary Processes....Pages 189-203
ARMA model....Pages 205-217
Discrete-Time Martingales....Pages 219-232
Brownian Motion and Diffusion Processes....Pages 233-253
Statistics for Poisson Processes....Pages 255-269
Statistics of Discrete-Time Stationary Processes....Pages 271-285
Statistics of Diffusion Processes....Pages 287-298
Back Matter....Pages 299-354
....