Foundations of Modern Probability (Probability and Its Applications)

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9780387953137: Foundations of Modern Probability (Probability and Its Applications)
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The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

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From the Back Cover:

From the reviews of the first editions: "... Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands." F.B. Knight, Mathematical Reviews
"...Indeed the monograph has the potential to become a (possibly even "the") major reference book on large parts of probability theory for the next decade or more." M. Scheutzow, Zentralblatt
"The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly...It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self-contained..." R.K. Getoor, Metrika
This new edition contains four new chapters as well as numerous improvements throughout the text.
Olav Kallenberg was educated in Sweden, where he received his Ph.D. in 1972 from Chalmers University. After teaching for many years at Swedish universities, he moved in 1985 to the U.S., where he is currently a Professor of Mathematics at Auburn University. He is known for his book "Random Measures" (4th edition, 1986) and for numerous research papers in all areas of probability. In 1977, he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. In 1991-94, he served as the Editor-in-Chief of "Probability Theory and Related Fields."

Review:

"The second edition of this admirable book has grown by well over one hundred pages, including such new material as: multivariate and ratio ergodic theorems, shift coupling, Palm distributions, entropy and information, Harris recurrence, invariant measures, strong and weak ergodicity, Strassen's LIL and the basic large deviation results. Also, a lot of existing material has been rewritten and expanded. I repeat a statement from my review of the first edition: "From the table of contents it is difficult to believe behind all these topics a streamlined readable text is at all possible. It is: Convince yourself." Those who own the first edition should make some extra space for this second edition. Those who do not yet own a copy: buy one!"

P.A.L. Embrechts in ISI Short Book Reviews, Vol. 22/3, December 2002

From the reviews of the first edition: "...Kallenberg's present book would have to qualify as the assimilation of probability par excellence. It is a great edifice of material, clearly and ingeniously presented, without any non-mathematical distractions. Readers wishing to venture into it may do so with confidence that they are in very capable hands." F.B. Knight, Mathematical Reviews

"... Indeed the monograph has the potential to become a (possibly even ``the'') major reference book on large parts of probability theory for the next decade or more." M. Scheutzow, Zentralblatt

"The theory of probability has grown exponentially during the second half of the twentieth century and the idea of writing a single volume that could serve as a general reference for much of the modern theory seems almost foolhardy. Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly. ... It is astonishing that a single volume of just over five hundred pages could contain so much material presented with complete rigor and still be at least formally self-contained..." R.K. Getoor, Metrica

From the reviews of the second edition:

"The first edition of the author’s magnum opus drew universal acclaim when it appeared in 1997 for its scope, clarity and precision. For the second edition ... Professor Kallenberg has added over a hundred pages in attempt to keep it up to date with the exponentially increasing body of knowledge which is probability theory. Moreover, certain sections ... have been comprehensively rewritten in order to be self-sufficient. ... This is an essential purchase for any serious probabilist." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (511), 2004)

"The first edition of this most outstanding monograph has been praised in many reviews. The second edition is a revised and enlarged version of the first ... . Of course, the praise for the first edition applies to the second edition as well. Nevertheless, it should be noted that the style in which this monograph is written is concise and particular. ... It has been said that the present monograph is a modern classic in probability theory, and this is true." (Klaus. D. Schmidt, Mathematical Reviews, Issue 2002 m)

"The second edition of this admirable book has grown by well over one hundred pages ... . Also, a lot of existing material has been rewritten and expanded. ... ‘From the table of contents it is difficult to believe behind all these topics a streamlined readable text is at all possible. It is: Convince yourself.’ Those who own the first edition should make some extra space for this second edition. Those who do not yet own a copy: buy one!" (P. A. L. Embrechts, Short Book Reviews, Vol. 22 (3), 2002)

"This second edition presents now even more material in the concise and elegant style of the former edition which by now has become a highly praised standard reference book for many areas of probability theory. ... The chapters of the first edition have been carefully revised and corrected so that it has become an even more accurate and reliable reference work. Starting a book with a page entitled ‘Praise for the first edition’ is always daring, but in the case of Kallenberg’s treatise indeed justified." (Markus Reiß, Zentralblatt Math, Vol. 996 (21), 2002)

"Foundations of Modern Probability is generally ... useful at a graduate level. ... It concision and abstractness makes it a useful reference." (Wordtrade, 2008)

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