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The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theory before entering into more advanced courses. The first six chapters focus on some central areas of what might be called pure probability theory: multivariate random variables, conditioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process as a means both to introduce stochastic processes and to apply many of the techniques introduced earlier in the text.
Students are assumed to have taken a first course in probability, though no knowledge of measure theory is assumed. Throughout, the presentation is thorough and includes many examples that are discussed in detail. Thus, students considering more advanced research in probability theory will benefit from this wide-ranging survey of the subject that provides them with a foretaste of the subject's many treasures.
The present second edition offers updated content, one hundred additional problems for solution, and a new chapter that provides an outlook on further areas and topics, such as stable distributions and domains of attraction, extreme value theory and records, and martingales. The main idea is that this chapter may serve as an appetizer to the more advanced theory.
Allan Gut is Professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is a member of the International Statistical Institute, the Bernoulli Society, the Institute of Mathematical Statistics, and the Swedish Statistical Society. He is an Associate Editor of the Journal of Statistical Planning and Inference and Sequential Analysis, a former Associate Editor of the Scandinavian Journal of Statistics, and the author of five other books including Probability: A Graduate Course (Springer, 2005) and Stopped Random Walks: Limit Theorems and Applications, Second Edition (Springer, 2009).
Students are assumed to have taken a first course in probability, though no knowledge of measure theory is assumed. Throughout, the presentation is thorough and includes many examples that are discussed in detail. Thus, students considering more advanced research in probability theory will benefit from this wide-ranging survey of the subject that provides them with a foretaste of the subject's many treasures.
The present second edition offers updated content, one hundred additional problems for solution, and a new chapter that provides an outlook on further areas and topics, such as stable distributions and domains of attraction, extreme value theory and records, and martingales. The main idea is that this chapter may serve as an appetizer to the more advanced theory.
Allan Gut is Professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is a member of the International Statistical Institute, the Bernoulli Society, the Institute of Mathematical Statistics, and the Swedish Statistical Society. He is an Associate Editor of the Journal of Statistical Planning and Inference and Sequential Analysis, a former Associate Editor of the Scandinavian Journal of Statistics, and the author of five other books including Probability: A Graduate Course (Springer, 2005) and Stopped Random Walks: Limit Theorems and Applications, Second Edition (Springer, 2009).
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From the reviews of the second edition:
"This is an excellent introductory book on random variables, with a wealth of examples and exercises. ... The material is very well organized ... . The text is remarkably well written, mathematically and aesthetically; layout and fonts make it a pleasant reading, and the examples are often enlightening. I think it will be a valuable support for students and instructors and it should definitely find a place in every good library." (Fabio Mainardi, The Mathematical Association of America, October, 2009)
"...A worthwhile addition to the textbook pool, one that will guide the student safely through to a point of competence and ability to embark on a more advanced study..." (International Statistical Review, 2010, 78, 1, 134-159)
"The book addresses a unique niche mathematically inclined students previously exposed to an introductory course in probability ... . The writing style is lucid and easy to follow. ... book is clearly directed toward mathematicians and the highly mathematically inclined scientist or engineer who might be induced to study the mathematics of probability or mathematical statistics. For those who find the classical mathematical pedagogy motivating or those requiring a comprehensive readable reference work on the mathematics of probability theory the book can be highly recommended." (Thomas D. Sandry, Technometrics, Vol. 53 (1), February, 2011)
"This book ... is intended as an introductory graduate level textbook in probability for statistics majors. ... This book provides an elaborate description and a collection of results in probability theory. ... The level of this book is suitable for a graduate course. Overall all concepts are well discussed with full mathematical rigor. ... has a good collection of most of the results related to probability theory, the price is very reasonable, and I will recommend this book to university mathematics and statisticslibraries." (Sounak Chakraborty, Journal of the American Statistical Association, Vol. 106 (495), September, 2011)
"This is an excellent introductory book on random variables, with a wealth of examples and exercises. ... The material is very well organized ... . The text is remarkably well written, mathematically and aesthetically; layout and fonts make it a pleasant reading, and the examples are often enlightening. I think it will be a valuable support for students and instructors and it should definitely find a place in every good library." (Fabio Mainardi, The Mathematical Association of America, October, 2009)
"...A worthwhile addition to the textbook pool, one that will guide the student safely through to a point of competence and ability to embark on a more advanced study..." (International Statistical Review, 2010, 78, 1, 134-159)
"The book addresses a unique niche mathematically inclined students previously exposed to an introductory course in probability ... . The writing style is lucid and easy to follow. ... book is clearly directed toward mathematicians and the highly mathematically inclined scientist or engineer who might be induced to study the mathematics of probability or mathematical statistics. For those who find the classical mathematical pedagogy motivating or those requiring a comprehensive readable reference work on the mathematics of probability theory the book can be highly recommended." (Thomas D. Sandry, Technometrics, Vol. 53 (1), February, 2011)
"This book ... is intended as an introductory graduate level textbook in probability for statistics majors. ... This book provides an elaborate description and a collection of results in probability theory. ... The level of this book is suitable for a graduate course. Overall all concepts are well discussed with full mathematical rigor. ... has a good collection of most of the results related to probability theory, the price is very reasonable, and I will recommend this book to university mathematics and statisticslibraries." (Sounak Chakraborty, Journal of the American Statistical Association, Vol. 106 (495), September, 2011)