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Introduction to Stochastic Processes (Dover Books on Mathematics), by Erhan Cinlar
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This clear presentation of the most fundamental models of random phenomena employs methods that recognize computer-related aspects of theory. The text emphasizes the modern viewpoint, in which the primary concern is the behavior of sample paths. By employing matrix algebra and recursive methods, rather than transform methods, it provides techniques readily adaptable to computing with machines.
Topics include probability spaces and random variables, expectations and independence, Bernoulli processes and sums of independent random variables, Poisson processes, Markov chains and processes, and renewal theory. Assuming some background in calculus but none in measure theory, the complete, detailed, and well-written treatment is suitable for engineering students in applied mathematics and operations research courses as well as those in a wide variety of other scientific fields. Many numerical examples, worked out in detail, appear throughout the text, in addition to numerous end-of-chapter exercises and answers to selected exercises.
- Sales Rank: #159499 in Books
- Published on: 2013-02-20
- Released on: 2013-01-24
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .94" w x 6.13" l, 1.40 pounds
- Binding: Paperback
- 416 pages
Most helpful customer reviews
20 of 23 people found the following review helpful.
Excellent
By Kalantari
It is an excellent introductory book in stochastic processes. But as the author have written in Afterword section of his book : "The two glaring omissions are the theories of Brownian motion and Martingales".
Anyway, I strongly recommend this book for begining of stochastic processes.
13 of 15 people found the following review helpful.
Fantastic for whom have knowledge of statistical and probability theories
By Augusto
It's a great book. Very well writen, full of proofs (some of them not so detailed, but perfectly understandable) and covers almost everything you need to know to start working with stochastic processes. However, a good knowledge about statistical and probability theories is more then desirable.
2 of 2 people found the following review helpful.
Excellent value, though just a bit formal
By Just a Guy
You can see by examining the table of contents that this book contains a very complete non-measure theoretic treatment of stochastic processes. The main text reads a bit "theorem-proofy" for my taste, and could arguably use some more diagrams (though no one else in the reviews has expressed such a view, so maybe that's just my problem). But this is partly offset by the large number of detailed examples.
Another plus: this is one of the few texts I've seen that treats the Bernoulli process explicitly - a whole chapter - rather than just starting with the Poisson process. I think this helps create a fuller picture of these processes, as the Bernoulli is essentially the discrete time analog (no "anti" pun intended!) of the Poisson.
The text goes on to present a very detailed treatment of Markov process in both discrete and continuous time, including a chapter on optimal stopping, which is not often treated at this level. You will find detailed treatments of branching and queuing models, renewal theory, and really just about everything that can be treated without measure theory. This is probably the best reference available on the subject at this level, especially in terms of content-to-price ratio.
Although I would supplement this book with a more elementary treatment (such as the excellent albeit pricey Bertsekas text, which contains some very easy to read chapters on stochastic processes), it is a valuable addition to the Dover catalog and should not be missed.
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