Introduction to the Theory of Random Processes (Dover Books on Mathematics)

Rating:
Summary: more like a survey of results then an introduction
Review: Although this claims to be an introductory text, it is more like a collection of results in stochastic processes. The notation is often impenetrable and there is not a uniform level of rigor in the text. Some results are presented in detail, and others sort of assume you've seen them before. There is no unifying theme here. It's hard to know where the author is going. A better rigorous book is "Stochastic Processes" by Doob.

Rating:
Summary: Excellent textbook
Review: I am giving 5 starts to counterbalance the unfair rating of 2 stars given by the other reader. Really, this book should be more around 4 stars.

To comment (but not dwell) on the previous reader's remarks: While the title is "Introduction to random processes", this book is indeed an introductory book and deals only with random processes, not probability theory. There is no misrepresentation here, the book claims no more than a course on probability theory as prerequisite. This is really needed, as the book does not present or even review the basic concepts of probability theory, which is fine because it is not a book on probability theory.

It is an introduction to random processes, and so uses a great deal of measure theory, hilbert and Lp spaces, carefully defines stochastic integration in terms of stochastic measure, the isomorphism between the hilbert space of random functions and the Lp space of continuous functions on [0,1] is used to motivate several topics.

Given the date at which this book was written (1969) it is no less than a masterpiece. It is a great exposition of the topic in its full generality, without sacrificing any of the important aspects, as is customarily done in physics/engineering and economics textbooks. This is a math book, and will appeal to mathematicians or scientists with a relatively strong undergraduate background in mathematics (you need to be at ease with analysis). So it does not target the general engineering audience, as the style of presentation is not for engineers (here you can't skip to chapter 7 right away, you need to start reading from page 1 and carefully prove the results one by one or else you will get lost quickly). There are better books out there for engineers, but this one is a solid mathematical introduction.

In general, you can't go wrong with a book on probability theory or random processes written by russian mathematicians. They are the kings in the field.