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Semi-Markov Processes and Reliability, by Nikolaos Limnios, G. Oprisan
Download Semi-Markov Processes and Reliability, by Nikolaos Limnios, G. Oprisan
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At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.
- Sales Rank: #3316616 in Books
- Brand: Brand: Birkhäuser
- Published on: 2001-02-16
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x .56" w x 7.01" l, 1.27 pounds
- Binding: Hardcover
- 222 pages
- ISBN13: 9780817641962
- Condition: USED - Like New
- Notes: 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!
Review
"The book presents an introductory and at the same time rather comprehensive treatment of semi-Markov processes and their applications to reliability theory. It also provides some general background (like measure theory, Markov processes and Laplace transform), which makes it accessible to a broader audience.… The book may be a useful tool for researchers and students interested in the theory of semi-Markov processes or its applications to reliability problems."
―Applications of Mathematics
Most helpful customer reviews
3 of 4 people found the following review helpful.
Everything is Clear to the Authors, if not to their Readers
By Paul Thurston
The authors state in the preface to their book that their goal is to provide "a thorough approach to semi-Markov processes and their applications in reliability". This is an ambitious objective for a 222 page text, since a large body of research on Semi-Markov processes has developed over the course of the last forty years or so.
In the opinion of this reviewer, Limnios & Oprisan never even come close to their grand objective. Their book is simply too short, too terse and too condensed to give a thorough treatment. The authors realized early on that they would need to reference the vast body of literature. It is strange to this reviewer that their treatment, copyright 2001, chooses as its main references out-of-print French texts by Neveu (1964) and Janssen (1969). The authors' choice of difficult-to-find auxiliary references makes their treatment that much less accessible.
The prerequisite list here is extensive. The authors claim that all that is required is an understanding of Markov Chains, like you might find in Stroock's An Introduction to Markov Processes or Norris' Markov Chains. Furthermore, the authors claim to cover the following list of topics in the first 29 pages of their book (which comprises Chapter 1): measure theory, Laplace transforms and continuous-time Markov processes. In reality, Limnios & Oprisan introduce (barely) these and other topics including: stopping times, the Optional Stopping Theorem, stationary stochastic processes, martingale theory, Ergodic theory, strong Markov Processes and renewal processes.
In order to get through the first chapter of Limnios & Oprisan, you'll need an excellent background in these topics. I recommend Rogers & Williams 800 page, two-volume set Diffusions, Markov Processes, and Martingales: Volume 1, Foundations and Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus.
Chapter 2 runs a mere 18 pages and purports to cover "Markov Renewal Processes". I stopped counting how many times the authors give references to out-of-print books in this chapter. I also lost count of the number of times the authors use the phrases "it is straightforward", "it is easy to show", or "it is well-known", in the context of mathematical problems having none of the above properties.
This book is useful to the reader in one sense: it whets the appetite for an understanding of Semi-Markov Processes and Reliability Theory and puts this reviewer in the market for a well-written book on the topic.
2 of 3 people found the following review helpful.
Good book for the right audience
By David Collins
The previous reviewer is correct that this is a very concise book, and the authors' statement in the preface that the material is "within the reach of those who have had a first course in probability" is a wild exaggeration. In reality, a good prerequisite would be some familiarity with measure-theoretic probability (e.g., including Lebesgue-Stieltjes integration and things like the Borel-Cantelli lemma) plus an acquaintance with stochastic processes at the level of Ross's Stochastic Processes. The book does contain some excellent appendices summarizing prerequisite topics, but these would only be suitable as a review, not to learn the material. Nevertheless, for the mathematically prepared (or those willing to really put some time and effort into it) this is an excellent (probably the best available) compendium of modern research on semi-Markov processes as applied to reliability and survival analysis.
Those more interested in applications and practical techniques for semi-Markov processes would find Flowgraph Models for Multistate Time-to-Event Data (Wiley Series in Probability and Statistics) of interest, or the chapter on semi-Markov processes in Fundamentals of Queueing Theory (Wiley Series in Probability and Statistics). But for researchers and others looking for a comprehensive treatment of theoretical issues, I would highly recommend this book
0 of 0 people found the following review helpful.
Great book
By Wee Meng Yeo
If you are serious about using semi Markov process to model reliability problems, this is definitely recommended! Kudos to the authors.
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