Average Reviews:
(More customer reviews)A remarkable well organised work. Every chapter contains all needed definitions and formulas, deep discussions of their meanings, proofs, and examples, all extraordinarily well blended. Also every chapter has two set of problems. The 'elementary problems' require applying the material covered. The 'problems' require to prove results, they provide an excellent ground to develop this skill. Some times the classic format proof-theorem is used, but usually the ideas flow: starting with a problem, introducing necessary definitions and finding a solution eventually a theorem is stated as a natural consequence.
The writing style is similar to the immortal 'Introduction to Probability Theory' and its Applications' by Feller, with a similar mixture of rigorous mathematics and probabilistic intuition. Though 'A First Course...' only reviews the basics, it has some common topics with Feller's and covers more advanced topics.
The style of the book is the perfect opposite of 'Introduction to probability Models' by Sheldon Ross, which is written in a much more flamboyant style, full of surprises and amazement, and requires the constant use of pencil and paper to follow the developments. These two sources can be combined to master the subject, despite the fact that students often find Ross's magnificent work too hard to follow. (Of course, some will say that it is a bad book, and that the professor can't teach...)
Even though 'A First Course...' is rarely used as a textbook (bad marketing?) after taking courses on multivariable calculus and basic probability, an undergraduate student is ready to read this book. Measure theory is barely used, and it is a surprise to see how far can one go using only probabilistic intuition. The book is also well suited to doctoral courses.
The consecutive chapters on Martingales and Brownian Motion are unparalleled, a unique collection of basic examples is used to illustrate results on Stopping Times and Convergence. Also, Measure Theory is introduced at this point in a very appealing manner. These concepts are then used to obtain classical results on Brownian Motion and other topics. Students interested in Stochastic Calculus (not covered in this book) and its many application in Finances, Engineering, Operations Research and Computer Science can acquire solid foundations here.
The chapter on Stationary Processes is also very special, it provides solid foundations for Econometrics and Time Series and it is often quoted in research papers.
In short: an excellent book to acquire solid foundations on Stochastic Processes, the only source I know for a simple and systematic introduction of certain topics.
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The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developingsimultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.
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