rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Stochastic Modeling
  name:
    name part: Lanchier, Nicolas.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 303 p. 63 illus., 6 illus. in color. online resource.
  abstract: 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™.
  table of contents: 1. Basics of Measure and Probability Theory -- 2. Distribution and Conditional Expectation -- 3. Limit Theorems -- 4. Stochastic Processes: General Definition -- 5. Martingales -- 6. Branching Processes -- 7. Discrete-time Markov Chains -- 8. Symmetric Simple Random Walks -- 9. Poisson Point and Poisson Processes -- 10. Continuous-time Markov Chains -- 11. Logistic Growth Process -- 12. Wright-Fisher and Moran Models -- 13. Percolation Models -- 14. Interacting Particle Systems -- 15. The Contact Process -- 16. The Voter Model -- 17. Numerical Simulations in C and Matlab.
  note: by Nicolas Lanchier.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical models
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9783319500386
  identifier: http://dx.doi.org/10.1007/978-3-319-50038-6
  record info:
    record creation date: 170201
    record change date: 20170201080527.0
    record identifier: 978-3-319-50038-6