Stochastics Back cover copy From the reviews of the first editions " 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. 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. 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.

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Stochastics Back cover copy From the reviews of the first editions " 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.

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. 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 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. After teaching for many years at Swedish universities, he moved in to the U. He is known for his book "Random Measures" 4th edition, and for numerous research papers in all areas of probability.

In , he was the second recipient ever of the prestigious Rollo Davidson Prize from Cambridge University. 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 do not yet own a copy: buy one! Yet this is precisely what Professor Kallenberg has attempted in the volume under review and he has accomplished it brilliantly. 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 This is an essential purchase for any serious probabilist.

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. Schmidt, Mathematical Reviews, Issue m "The second edition of this admirable book has grown by well over one hundred pages Embrechts, Short Book Reviews, Vol.

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.

It concision and abstractness makes it a useful reference.

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## Foundations of Modern Probability

Main Foundations of Modern Probability Foundations of Modern Probability Olav Kallenberg This book is unique for its broad and yet comprehensive coverage of modern probability theory, ranging from first principles and standard textbook material to more advanced topics. In spite of the economical exposition, careful proofs are provided for all main results. After a detailed discussion of classical limit theorems, martingales, Markov chains, random walks, and stationary processes, the author moves on to a modern treatment of Brownian motion, L vy processes, weak convergence, It calculus, Feller processes, and SDEs. The more advanced parts include material on local time, excursions, and additive functionals, diffusion processes, PDEs and potential theory, predictable processes, and general semimartingales.

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