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Stochastic Modeling

  • Nicolas Lanchier

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Probability theory

    1. Front Matter
      Pages 1-1
    2. Nicolas Lanchier
      Pages 3-24
    3. Nicolas Lanchier
      Pages 25-40
    4. Nicolas Lanchier
      Pages 41-56
  3. Stochastic processes

    1. Front Matter
      Pages 57-57
    2. Nicolas Lanchier
      Pages 59-63
    3. Nicolas Lanchier
      Pages 65-91
    4. Nicolas Lanchier
      Pages 93-99
    5. Nicolas Lanchier
      Pages 101-128
    6. Nicolas Lanchier
      Pages 129-139
    7. Nicolas Lanchier
      Pages 141-160
    8. Nicolas Lanchier
      Pages 161-189
  4. Special models

    1. Front Matter
      Pages 191-191
    2. Nicolas Lanchier
      Pages 193-201
    3. Nicolas Lanchier
      Pages 203-218
    4. Nicolas Lanchier
      Pages 219-234
    5. Nicolas Lanchier
      Pages 235-244
    6. Nicolas Lanchier
      Pages 245-258
    7. Nicolas Lanchier
      Pages 259-268
    8. Nicolas Lanchier
      Pages 269-293
  5. Back Matter
    Pages 295-303

About this book

Introduction

Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes.

The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright–Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab™.

Keywords

Martingales Markov Chains Poisson Processes Symmetric Random Walks Branching Processes Wright-Fisher Model Percolation Models Contact Process Vorter Model Numerical Simulations

Authors and affiliations

  • Nicolas Lanchier
    • 1
  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-50038-6
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-50037-9
  • Online ISBN 978-3-319-50038-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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