Foundations of Modern Probability

Book Preface

Foundations of Modern Probability Olav Kallenberg Springer Preface Some thirty years ago it was still possible, as Lo` eve so ably demonstrated, to write a single book in probability theory containing practically everything worth knowing in the subject. The subsequent development has been ex- plosive, and today a corresponding comprehensive coverage would require a whole library. Researchers and graduate students alike seem compelled to a rather extreme degree of specialization. As a result, the subject is threatened by disintegration into dozens or hundreds of subfields. At the same time the interaction between the areas is livelier than ever, and there is a steadily growing core of key results and techniques that every probabilist needs to know, if only to read the literature in his or her own field. Thus, it seems essential that we all have at least a general overview of the whole area, and we should do what we can to keep the subject together. The present volume is an earnest attempt in that direction. My original aim was to write a book about “everything.” Various space and time constraints forced me to accept more modest and realistic goals for the project. Thus, “foundations” had to be understood in the narrower sense of the early 1970s, and there was no room for some of the more recent developments. I especially regret the omission of topics such as large de- viations, Gibbs and Palm measures, interacting particle systems, stochastic differential geometry, Malliavin calculus, SPDEs, measure-valued diffusions, and branching and superprocesses. Clearly plenty of fundamental and in- triguing material remains for a possible second volume. Even with my more limited, revised ambitions, I had to be extremely selective in the choice of material. More importantly, it was necessary to look for the most economical approach to every res…