β Scribed by Denis Bosq, Hung T. Nguyen (auth.)
No coin nor oath required. For personal study only.
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 (MathΒ ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on motiΒ 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 mathΒ ematically?". The exercises at the end of each lesson will deepen the stuΒ 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.
Front Matter....Pages i-x
Basic Probability Background....Pages 1-32
Modeling Random Phenomena....Pages 33-44
Discrete β Time Markov Chains....Pages 45-77
Poisson Processes....Pages 79-94
Continuous β 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
Probability Theory and Stochastic Processes; Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Signal, Image and Spe
π SIMILAR VOLUMES
Covering both theory and applications, this collection surveys the role of probabilistic models and statistical techniques in image analysis and processing, develops likelihood methods for inference about parameters.
<p>This work is an overview of statistical inference in stationary, discrete time stochastic processes. Results in the last fifteen years, particularly on non-Gaussian sequences and semi-parametric and non-parametric analysis have been reviewed. The first chapter gives a background of results on mar
This was the assigned text for an upper-level graduate course I took in Advanced Operations Research. My classmates and I despised it. It's disjointed, inconsistent, with unilluminating, half-worked examples (when there are any examples at all). Even the PhD candidates denounced it as unreadable. Al
The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of s