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Brownian Models of Performance and Control

$49.99 (P)

  • Date Published: December 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107018396

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  • Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queueing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald-Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models, or Brownian filtering models.

    • Applications in business and economics are interwoven with the development of basic theory
    • The treatment is compact, narrowly focused and briskly paced for accessibility to non-mathematicians
    • Basic comprehension is enhanced by essential abstract mathematical concepts and simple notation
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    Product details

    • Date Published: December 2013
    • format: Hardback
    • isbn: 9781107018396
    • length: 205 pages
    • dimensions: 235 x 158 x 20 mm
    • weight: 0.45kg
    • contains: 20 b/w illus. 2 tables 50 exercises
    • availability: Available
  • Table of Contents

    1. Brownian motion
    2. Stochastic storage models
    3. Further analysis of Brownian motion
    4. Stochastic calculus
    5. Optimally stopping a Brownian motion
    6. Reflected Brownian motion
    7. Optimal control of Brownian motion
    8. Brownian models of dynamic inference
    9. Further examples
    Appendix A. Stochastic processes
    Appendix B. Real analysis.

  • Author

    J. Michael Harrison, Stanford University, California
    J. Michael Harrison has developed and analyzed stochastic models in several different domains related to business, including mathematical finance and processing network theory. His current research is focused on dynamic models of resource sharing, and on the application of stochastic control theory in economics and operations. Professor Harrison has been honored by the Institute for Operations Research and Management Science (INFORMS) with its Expository Writing Award (1998), the Lanchester Prize for best research publication (2001), and the John von Neumann Theory Prize (2004); he was elected to the National Academy of Engineering in 2008. He is a fellow of INFORMS and of the Institute for Mathematical Statistics.

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