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A Course in Stochastic Processes

Stochastic Models and Statistical Inference

  • Book
  • © 1996

Overview

Authors:
  1. Denis Bosq

    1. Institut de Statistique, Université Pierre et Marie Curie, Paris, France

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    You can also search for this author in PubMed   Google Scholar

  2. Hung T. Nguyen

    1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Theory and Decision Library B (TDLB, volume 34)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Basic Probability Background

    • Denis Bosq, Hung T. Nguyen
    Pages 1-32

  3. Modeling Random Phenomena

    • Denis Bosq, Hung T. Nguyen
    Pages 33-44

  4. Discrete — Time Markov Chains

    • Denis Bosq, Hung T. Nguyen
    Pages 45-77

  5. Poisson Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 79-94

  6. Continuous — Time Markov Chains

    • Denis Bosq, Hung T. Nguyen
    Pages 95-116

  7. Random Walks

    • Denis Bosq, Hung T. Nguyen
    Pages 117-146

  8. Renewal Theory

    • Denis Bosq, Hung T. Nguyen
    Pages 147-169

  9. Queueing Theory

    • Denis Bosq, Hung T. Nguyen
    Pages 171-188

  10. Stationary Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 189-203

  11. ARMA model

    • Denis Bosq, Hung T. Nguyen
    Pages 205-217

  12. Discrete-Time Martingales

    • Denis Bosq, Hung T. Nguyen
    Pages 219-232

  13. Brownian Motion and Diffusion Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 233-253

  14. Statistics for Poisson Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 255-269

  15. Statistics of Discrete-Time Stationary Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 271-285

  16. Statistics of Diffusion Processes

    • Denis Bosq, Hung T. Nguyen
    Pages 287-298

  17. Back Matter

    Pages 299-354
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Keywords

About this book

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.

Authors and Affiliations

  • Institut de Statistique, Université Pierre et Marie Curie, Paris, France

    Denis Bosq

  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Hung T. Nguyen

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