SpringerBriefs in Mathematics

Analyzing Markov Chains using Kronecker Products

Theory and Applications

Authors: Dayar, Tugrul

  • First to provide a solely Kronecker product based treatment of Markov chain analysis
  • The subject matter is interdisciplinary and at the intersection of applied mathematics, specifically numerical linear algebra and computational probability, and computer science
  • The exposition is concise and rigorous, yet it tries to be complete and touches almost all relevant aspects without being too technical.
see more benefits

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-4190-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-4189-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.

Reviews

From the reviews:

“Dayar’s book on Kronecker products for Markov processes addresses an important topic which, up to now, has not been thoroughly discussed as a single entity in the literature. … The book has numerous examples throughout to illustrate the results and methods which the author presents. … the book is a valuable tool for learning to apply Kronecker representation to continuous time Markov chains.” (Myron Hlynka, Mathematical Reviews, May, 2013)

Table of contents (6 chapters)

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-4190-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-4189-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Analyzing Markov Chains using Kronecker Products
Book Subtitle
Theory and Applications
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Tugrul Dayar
eBook ISBN
978-1-4614-4190-8
DOI
10.1007/978-1-4614-4190-8
Softcover ISBN
978-1-4614-4189-2
Series ISSN
2191-8198
Edition Number
1
Number of Pages
IX, 86
Number of Illustrations and Tables
3 b/w illustrations
Topics