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.
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