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Most Helpful Customer Reviews
16 of 18 people found the following review helpful:
5.0 out of 5 stars
Very educational, very smooth, well written,
By SamBK (United States) - See all my reviews
This review is from: Finite Markov Chains: With a New Appendix "Generalization of a Fundamental Matrix" (Undergraduate Texts in Mathematics) (Hardcover)
I have been familiar with this book for over 8 years and I should say this is one of the best educational and practical books you can find about Markov chains. The book claims to be written for undergraduates, but it is marvelously useful for graduate students too.
The book starts by definition of Markov chains and gradually gets into more advanced definitions like absorbing states, cyclical chains, ergodicity ... Then there are these little lemmas and theorems about different aspects of Markov chains like what is the expected time of sitting at a transient state, what is the expected time of returning to the same state, etc. The proofs are nicely presented and there is a whole lot of application for those theorems in all fields that use Markov chains (like engineering, economics, ...). The book is actually abstract math and doesn't get very specialized at any time. I think this is a book one wants to start learning Markov chains from or keep in shelf for frequent references. I actually used some of its derivations in my own Master's thesis and got a lot of interesting feedbacks on what I did. Now is your turn!
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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single ergodic set, first passage matrix, probability vector fixed point, lumpable with respect, weak lumpability, fixed probability vector, independent trials process, lumped chain, lumped process, regular transition matrix, condition for lumpability, absorbing chain, ergodic chain, single absorbing state, finite stochastic process, ergodic sets, cyclic class, ergodic state, new transition matrix, limiting matrix, limiting vector, initial probability vector, trials chain, limiting covariances, statement whose truth value Key Phrases - Capitalized Phrases (CAPs): (learn more)
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single ergodic set, first passage matrix, probability vector fixed point, lumpable with respect, weak lumpability, fixed probability vector, independent trials process, lumped chain, lumped process, regular transition matrix, condition for lumpability, absorbing chain, ergodic chain, single absorbing state, finite stochastic process, ergodic sets, cyclic class, ergodic state, new transition matrix, limiting matrix, limiting vector, initial probability vector, trials chain, limiting covariances, statement whose truth value Key Phrases - Capitalized Phrases (CAPs): (learn more)
World Series New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
19
books
cite this book:
See all 19 books citing this book
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Back Matter
- Probability: An Introduction with Statistical Applications by John J. Kinney in Back Matter
- Fourier Analysis on Finite Groups and Applications (London Mathematical Society Student Texts) by Audrey Terras in Back Matter
- Introduction to Dynamic Systems: Theory, Models, and Applications by David G. Luenberger in Back Matter
- Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition by Kishor Shridharbhai Trivedi in Back Matter
See all 19 books citing this book
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