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Stochastic-Process Limits

Stochastic-Process Limits


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About the Book

This book is about stochastic-process limits - limits in which a sequence of stochastic processes converges to another stochastic process. These are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book emphasizes the continuous-mapping approach to obtain new stochastic-process limits from previously established stochastic-process limits. The continuous-mapping approach is applied to obtain heavy-traffic-stochastic-process limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavy-traffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. This book was the recipient of the 2003 INFORMS Frederick W. Lanchester Prize, awarded annually by the Institute for Operations Research and the Management Sciences (INFORMS) for the best contribution to operations research and the management sciences published in English.

Review :
From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queueing theory is beneficial to prospective readers. However, the first five chapters do provide an informal introduction to stochastic-process limits and their applications to queues, and is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews, Vol. 22/3, December 2002 "Wonderful work has been done by numerous mathematicians providing the fundamentals of the theory of function fields in one variable at least over finite fields in equivalence to the established theory of numbers. Everybody who wants to get in touch with these results should have a look into this book. For example, Chapter VII gives a beautiful application of the Riemann-Hurwitz theorem to the proof of the ABC-conjecture . The audience eagerly awaits a second part of this book ." (Bernd Richter, Zentralblatt MATH, Vol. 1043 (18), 2004) "The book covers a reasonable choice of material concerning the arithmetic of function fields that can be treated in a one-year introductory course on the graduate level. The text is largely self-contained. Both in the large (choice and arrangement of the material) and in the details (accuracy and completeness of proofs, quality of explanations and motivating remarks), the author did a marvellous job. Number theory in function fields will be the distinguished textbook in the field for many years." (Ernst-Ulrich Gekeler, Mathematical Reviews, 2003 d) "The interplay over the years between global function fields and number fields has been intense and extremely fruitful. Number theory in function fields does an excellent job of introducing these ideas. It will be a welcome resource for any number theorist, and it should become a standard text for graduate students in the area. There is a great pedagogical advantage in viewing difficu


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Product Details
  • ISBN-13: 9781475777215
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 254 mm
  • Weight: 1080 gr
  • ISBN-10: 1475777213
  • Publisher Date: 15 Jan 2014
  • Binding: Paperback
  • Spine Width: 32 mm
  • Width: 178 mm


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